179
179
Nov 14, 2013
11/13
by
Eduardo Fradkin
texts
eye 179
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We will now discuss how to represent physical measurements. All local physical measurements of a macroscopic quantum (many-body) system amount in practice to a process in which a localized disturbance is created by anapplied external force, in the neighborhood of some point _r at some time t, and the response of the system is then measured at some other point _r_attome later time t_> t. On the other hand, in many cases we also will be interested in the global response of a system to an...
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
Source: http://www.flooved.com/reader/2881
228
228
Nov 14, 2013
11/13
by
David Tong
texts
eye 228
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comment 0
We would now like to quantize the Dirac Lagrangian,...We will proceed naively and treat _ as we did the scalar �eld. But we�ll see that things go wrong and we will have to reconsider how to quantize this theory.
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/2965
194
194
Nov 14, 2013
11/13
by
Eduardo Fradkin
texts
eye 194
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comment 0
In the past chapter we gave a summary of the Hilbert space picture of Quantum Mechanics and of a Scalar Quantum Field Theory. Here we will present the Path Integral picture of Quantum Mechanics and Scalar Quantum Field Theory.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
Source: http://www.flooved.com/reader/2876
282
282
Nov 14, 2013
11/13
by
David Tong
texts
eye 282
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In this �rst section we will discuss various aspects of classical �elds. We will cover only the bare minimum ground necessary before turning to the quantum theory, and will return to classical �eld theory at several later stages in the course when we need to introduce new ideas.
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/2961
135
135
Nov 14, 2013
11/13
by
Eduardo Fradkin
texts
eye 135
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Let us consider now the problem of a system of N identical non-relativistic particles. For the sake of simplicity I will assume that the physical state of each particle j is described by its position... relative to some reference frame. This case is easy to generalize.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
Source: http://www.flooved.com/reader/2877
99
99
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 99
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
Source: http://www.flooved.com/reader/3163
289
289
Nov 14, 2013
11/13
by
Eduardo Fradkin
texts
eye 289
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comment 0
The purpose of this course, Physics 582, is two fold. Here I will to introduce Field Theory as a framework for the study of systems with a very large number of degrees of freedom, N _ �. On the other hand, I will also introduce and develop the tools that will allow us to treat such systems. Systems that involve a large (in fact in�nite) number of coupled degrees of freedom arise in many areas of Physics, notably in High Energy and in Condensed Matter Physics, among others. Although the...
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
Source: http://www.flooved.com/reader/2870
108
108
Nov 14, 2013
11/13
by
Eduardo Fradkin
texts
eye 108
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We will begin now the discussion of our main subject of interest: the role of quantum mechanical �uctuations in systems with in�ntely many degrees of freedom. We will begin with a brief overview of quantum mechanics of a single particle.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
Source: http://www.flooved.com/reader/2875
184
184
Nov 14, 2013
11/13
by
David Tong
texts
eye 184
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comment 0
Canonical Quantization: In quantum mechanics, canonical quantization is a recipe that takes us from the Hamiltonian formalism of classical dynamics to the quantum theory. The recipe tells us to take the generalized coordinates qa and their conjugate momenta pa and promote them to operators. The Poisson bracket structure of classical mechanics morphs into the structure of commutation relations between operators, so that, in units with _ = 1,...
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/2962
205
205
Nov 14, 2013
11/13
by
David Tong
texts
eye 205
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comment 0
The purpose of this course is to answer these questions. We shall see that the second viewpoint above is the most useful: the �eld is primary and particles are derived concepts, appearing only after quantization. We will show how photons arise from the quantization of the electromagnetic �eld and how massive, charged particles such as electrons arise from the quantization of matter �elds. We will learn that in order to describe the fundamental laws of Nature, we must not only introduce...
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/2960
170
170
Nov 14, 2013
11/13
by
David Tong
texts
eye 170
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comment 0
The free �eld theories that we�ve discussed so far are very special: we can determine their spectrum, but nothing interesting then happens. They have particle excitations, but these particles don�t interact with each other. Here we�ll start to examine more complicated theories that include interaction terms. These will take the form of higher order terms in the Lagrangian. We�ll start by asking what kind of small perturbations we can add to the theory. For example, consider the...
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/2963
185
185
Nov 14, 2013
11/13
by
Eduardo Fradkin
texts
eye 185
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comment 0
In the past lectures we have considered the properties of a number of �eld theories that describe physical systems isolated from the outside world. However,the only way to investigate the properties of a physical system is to interact withit. Thus, we must consider physical systems which somehow are coupled to theirsurroundings. We will have two situations in mind. In one case, we will look atthe problem of the interaction of states of an isolated system, i.e., a scatteringproblem. In this...
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
Source: http://www.flooved.com/reader/2871
91
91
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 91
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3168
110
110
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 110
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3176
110
110
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 110
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3178
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150
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 150
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3155
191
191
Nov 14, 2013
11/13
by
David Tong
texts
eye 191
favorite 0
comment 0
All lecture courses on string theory start with a discussion of the point particle. Ours is no exception. We�ll take a �ying tour through the physics of the relativistic point particle and extract a couple of important lessons that we�ll take with us as we move onto string theory.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3188
84
84
Nov 14, 2013
11/13
by
David Tong
texts
eye 84
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comment 0
So far, we�ve only discussed strings propagating in �at spacetime. In this section we will consider strings propagating in di_erent backgrounds. This is equivalent to having di_erent CFTs on the world sheet of the string.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3183
194
194
Nov 14, 2013
11/13
by
David Tong
texts
eye 194
favorite 0
comment 0
At the beginning of the last chapter, we stressed that there are two very di_erent interpretations of conformal symmetry depending on whether we�re thinking of a �xed 2d background or a dynamical 2d background. In applications to statistical physics, the background is �xed and conformal symmetry is a global symmetry. In contrast, instring theory the background is dynamical. Conformal symmetry is a gauge symmetry, a remnant of di_eomorphism invariance and Weyl invariance.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3186
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115
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 115
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3160
79
79
Nov 14, 2013
11/13
by
David Tong
texts
eye 79
favorite 0
comment 0
In this section, we will consider the simplest compacti�cation of the bosonic string
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3180
82
82
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 82
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3159
92
92
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 92
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3177
112
112
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 112
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3158
221
221
Nov 14, 2013
11/13
by
David Tong
texts
eye 221
favorite 1
comment 0
These lectures are aimed at beginning graduate students. They assume a working knowledge of quantum �eld theory and general relativity. The lectures were given over one semester and are based broadly on Vol. 1 of the book by Joe Polchinski. I inherited the course from Michael Green whose notes were extremely useful. I also bene�ted enormously from the insightful and entertaining video lectures by Shiraz Minwalla.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3182
104
104
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 104
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3161
113
113
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 113
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3156
139
139
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 139
favorite 0
comment 0
The aim of this course is to develop the machinery to explore the properties of quantum systems with very large or in�nite numbers of degrees of freedom. To represent such systems it is convenient to abandon the language of individual elementary particles and speak about quantum �elds. In this lecture, we will consider the simplest physical example of a free or non-interacting many-particle theory theory which will exemplify the language of classical and quantum �elds. Our starting point...
Topics: Physics, Condensed Matter, Particle Physics and Fields, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/3059
488
488
Nov 14, 2013
11/13
by
David Tong
texts
eye 488
favorite 0
comment 0
In this section we �nally get to quantum electrodynamics (QED), the theory of light interacting with charged matter. Our path to quantization will be as before: we start with the free theory of the electromagnetic �eld and see how the quantum theory gives rise to a photon with two polarization states. We then describe how to couple the photon to fermions and to bosons.
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/3077
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130
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 130
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes, D...
Source: http://www.flooved.com/reader/3171
516
516
Nov 14, 2013
11/13
by
Roberto Casalbuoni
texts
eye 516
favorite 1
comment 0
Aim of this course is to extend ordinary quantum mechanics, which describes nonrelativistic particles in interaction with given forces, to the relativistic case where forces are described by �elds, as for the electromagnetic case. The most relevant di_erences between the two cases are that the forces become dynamical degrees of freedom, and that one needs a relativistic treatment of the problem. In order to get a consistent description we will need to quantize the �eld degrees of freedom....
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/3071
152
152
Nov 14, 2013
11/13
by
David Tong
texts
eye 152
favorite 0
comment 0
We would now like to quantize the Dirac Lagrangian. We will proceed naively and treat _ as we did the scalar �eld. But we�ll see that things go wrong and we will have to reconsider how to quantize this theory.
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/3076
185
185
Nov 14, 2013
11/13
by
David Tong
texts
eye 185
favorite 0
comment 0
Here we�ll start to examine more complicated theories that include interaction terms. These will take the form of higher order terms in the Lagrangian. We�ll start by asking what kind of small perturbations we can add to the theory. For example, consider the Lagrangian for a real scalar �eld,
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/3074
112
112
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 112
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes, D...
Source: http://www.flooved.com/reader/3173
149
149
Nov 14, 2013
11/13
by
David Tong
texts
eye 149
favorite 0
comment 0
Here I summarize the key concepts that you will need throughout this course. This will also serve to set conventions and notations. If you�re not comfortable with any of these concepts or terms, you should review a suitable book as soon as possible.
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
Source: http://www.flooved.com/reader/3075
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104
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 104
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes, D...
Source: http://www.flooved.com/reader/3172
123
123
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 123
favorite 0
comment 0
We have seen how the elementary excitations of the quantum chain can be presented in terms of new elementary quasi-particles by the ladder operator formalism. Can this approach be generalised to accommodate other many-body systems? The answer is provided by the method of second quantisation � an essential tool for the development of interacting many-body �eld theories. The �rst part of this section is devoted largely to formalism �the second part to applications aimed at developing...
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3064
91
91
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 91
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Field...
Source: http://www.flooved.com/reader/3179
112
112
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 112
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Field...
Source: http://www.flooved.com/reader/3166
158
158
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 158
favorite 0
comment 0
Could formulate many-body propagator (Green function), but here, convenient to focus on partition function.
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3054
123
123
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 123
favorite 0
comment 0
The aim of this lecture is to explore the nature of the ground state and the character of the elementary excitation spectrum in the condensed phase.
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3069
217
217
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 217
favorite 0
comment 0
The aim of this section is to introduce the language and machinery of classical and quantum �eld theory through its application to the problem of lattice vibrations in a solid. In doing so, we will become acquainted with the notion of symmetry breaking, universality, elementary excitations and collective modes � concepts which will pervade much of thecourse.
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3048
156
156
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 156
favorite 0
comment 0
We have seen that the quantum Heisenberg Ferromagnetic spin chain is characterised by a magnetically ordered ground state with free particle-like elementary spin wave excitations� magnons. What happens in the antiferromagnetic system?
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3068
142
142
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 142
favorite 0
comment 0
In this chapter, the concept of path integration is generalized to integration over quantum �elds. Speci�cally we will develop an approach to quantum �eld theory that takes a sits starting point an integration over all con�gurations of a given �eld, weighted by anappropriate action. To emphasize the importance of the formulation which, methodologiccally, represents the backbone of the remainder of the text, we have pruned the discussion to focus only on the essential elements. This...
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3047
106
106
Nov 14, 2013
11/13
by
Alan Guth;Barton Zwiebach
texts
eye 106
favorite 0
comment 0
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Field...
Source: http://www.flooved.com/reader/3164
149
149
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 149
favorite 0
comment 0
Having established that the low energy properties of the atomic chain are represented by a free scalar classical �eld theory, we now turn to the formulation of the quantum system.
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3063
148
148
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 148
favorite 1
comment 0
According to band picture of non-interacting electrons, a 1/2-�lled band of states is metallic. But strong Coulomb interaction of electrons can lead to a condensation or crystallisation of the electron gas into a solid, magnetic, insulating phase � Mott transition. Here we employ the second quantisation to explore the basis of this phenomenon.
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3066
125
125
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 125
favorite 0
comment 0
Previously, we have seen how the functional �eld integral technique can be developed to explore the impact of the electronic degrees of freedom on the e_ective Coulomb interaction in a metal. However, our considerations did not engage any non-trivial mean-�elds: the platform of the non-interacting electron system remains adiabatically connected to that ofthe weakly interacting system. In the following we will explore a problem in which the development of a non-trivial ground state � the...
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3058
126
126
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 126
favorite 0
comment 0
Connection of Path Integral to Classical Statistical Mechanics Consider �exible string held under constant tension and con�ned to �gutter� potential...
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3050
175
175
Nov 14, 2013
11/13
by
Ben Simons
texts
eye 175
favorite 1
comment 0
How can phenomena of QM tunneling be described by Feynman path integral?
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
Source: http://www.flooved.com/reader/3052
