Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...

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What assumptions about the action do we make or give up in transitioning from classical mechanics to quantum mechanics to quantum field theory?

I am reading Quantum Field Theory for the Gifted Amateur and I feel I don't have a good grasp as to how the Lagrangian and the action are used differently in (1) classical mechanics (2) quantum ...
3
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3answers
992 views

what causes virtual particle pair production to not occur in the space occupied by matter?

Are virtual particles only popping in and out of existence where the local energy density is below a certain point? What I wonder is, does any kind of matter prevent the pairs from appearing? Is ...
6
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1answer
156 views

What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
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2answers
117 views

If path integrals aren't well-defined, how can they have any physical meaning?

I am confused about a particular point about the nature of path integration. According to what I've read, what we really mean when we say functional integration is \begin{equation} ...
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91 views

(Euclideanized) QFT on $S^d$ vs $S^{d-1}\times S^1$

Broadly I would like to understand what is the difference in the physical interpretation of a (Euclideanized) QFT which is on space-time $S^d$ and which is on a space-time $S^{d-1}\times S^1$. In ...
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9answers
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Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
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52 views

Feynman diagrams with classical apparatus on the perturbative region

on QFT, one usually simplifies the interaction between fields and classical apparatus (sources, detectors, etc.) by assuming the classical devices only interact with the asymptotic on-shell states ...
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1answer
483 views

Superficial Degree of Divergence for Feynman Diagrams

The superficial degree of divergence for a diagram is defined as the power of $k$ in the nominator minus the power of $k$ in the denominator. It is written to be equal to $4\times$ ...
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1answer
55 views

Outside of string theory, can exchange particles be understood as being one-dimensional?

I'm pretty new to quantum, without any formal education therein, so forgive my general layman ignorance when I ask how it is that point-like exchange particles can be modeled in Feynman diagrams as ...
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36 views

Quantizing field with anti-periodic boundary condition

This is a naive question about a possible toy model in QFT. In particular, I am trying to find a simple model where spin-statistics theorem holds. One can construct a 1+1 dimensional classical ...
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1answer
49 views

Every Relativistic Field Satifies the Klein-Gordon Equation?

I've read that every relativistic scalar field (and in some sense, any field) satisfies the Klein-Gordon equation. Is the reasoning for this just based on the quantum mechanical substitution of $E\to ...
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3answers
280 views

Dimensions in lagrangian potential

According to Mankowski flat space dimensions We can write, $$L= \int \text{dt} \text d^d{x} \left[ \frac{1}{2} \dot\phi^2 - \frac{1}{2} \left(\frac{\partial \phi}{\partial r} \right)^2 ...
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97 views

Does equality of operators on vacuum imply equality of operators on the whole space?

Consider a field operator $\Phi(x)$ which generates states from the vacuum such as $$ \tag 1 | x \rangle = \Phi(x) | 0 \rangle.$$ Consider also how a translation is implemented on such a state: $$ ...
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0answers
32 views

Fujikawa method for arbitrary transformations

When the Fujikawa method is presented in every book I've read so far, the transformation is initially written as $e^{i\chi (x) \gamma^{5}}$. The trace of $i\chi(x)\gamma^{5}$ is done by including a ...
3
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1answer
197 views

Fierz identity for Weyl spinors in tensor currents

Using Fierz identity I found that certain four-fermion operator with left $l_i$ and right-chiral $r_i$ Weyl spinors vanish $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
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1answer
89 views

Quick question regarding Wick's theorem

Let $T\{...\}$ denote time-ordering, $N\{...\}$ normal-ordering and $\left<ab\right>$ be the propagator. Wick's theorem states that $$ T\{ab\} = N\{ab\} + \left<ab\right>. $$ I now ...
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63 views

Does point group symmetry also act within “spin space” for a lattice spin system?

As an example, let's consider a quantum spin system on a 2D square lattice. The lattice point group symmetries include $C_4$ rotation, parities, etc.... And let's take $C_2$ symmetry (2-fold rotation) ...
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1answer
46 views

Delta functional in path integrals - reference needed

In a few articles dealing with path integral quantization I came across some calculations where apparently identities of the form \begin{equation} \int (\mathcal{D}\Phi)\, ...
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2answers
1k views

Irreducible Representations Of Lorentz Group

In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64. He define states as ...
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4answers
5k views

What would the collision of two photons look like?

Could someone explain me what will the collision of two photons look like? Will they behave like: Electromagnetic waves, they will interpher with each other and keep they wave nature Particles and ...
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6answers
6k views

What is a complete book for quantum field theory?

I am searching for a complete and comprehensive book for QFT. What is, in your opinion, a good one?
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0answers
96 views

Questions regarding $D=4 $ ${\cal N}=4$ supersymmetric Yang-Mills

I have some questions regarding the $D=4 $ ${\cal N}=4$ super-Yang-Mills theory (the one with a really long action which can be acquired by compactifying the 10-dimensional ${\cal N}=1$ theory). I ...
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2answers
139 views

Why is the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group realized as the vector space of complex $2\times 2$ matrices?

Why can we write an arbitrary object $v_{a \dot{b} }$ our transformations in this basis act on as $$ v_{a \dot{b} } = v_{\nu} \sigma^{ \nu}_{a \dot{b} } = v^0 \begin{pmatrix} 1&0 \\ 0&1 ...
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1answer
50 views

Soft-Supersymmetry Mass (Direct contact term)

I found this term/operator in some papers that can generate masses, e.g Riva-Biggio-Pomarol(2012), Fox-Nelson-Weiner $\int d^4\theta \frac{X^\dagger X}{M^2}Q^\dagger Q$ Could anyone explain about ...
3
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1answer
611 views

Why doesn't the Klein-Gordon equation allow for conservation of probability?

I read somewhere that the Klein-Gordon equation doesn't allow for conservation of probability. Can someone prove this mathematically?
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1answer
53 views

Need help understanding the quantization procedure in QFT for the Klein-Gordon equation

I am having some conceptual issues with the quantization process in QFT. So we define a particle as a collection of functions $\mathcal{H}$ that satisfy some differential equation (more specifically a ...
7
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1answer
1k views

Schrodinger equation from Klein-Gordon?

One can view QM as a 1+0 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrodinger's equation from Klein-Gordon's one. Assuming a ...
6
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3answers
533 views

Why is the Klein Gordon equation of second order in time?

I was wondering if there is any way to interpret the fact that the Klein Gordon equation is a 2nd order PDE in time. I mean, normally you would expect that as soon as you fix the initial wavefunction, ...
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2answers
132 views

What are the problems in trying to interpret the Klein-Gordon equation as a single particle equation?

What is the problem if we try to interpret KG equation as a single particle equation? Also I wish to know whether the born interpretation of wavefunction is applicable in relativistic quantum ...
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2answers
2k views

How can one find the energy eigenfunctions of a particle in a finite square well via the Klein-Gordon equation?

It is said that Klein-Gordon equation is a relativistic version of the Schrodinger equation. In Schrodinger equation, it is straightforward to include potential energy. But for K-G eqn things seem to ...
10
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3answers
2k views

What are the calculations for Vacuum Energy?

In wiki the Vacuum Energy in a cubic meter of free space ranges from $10^{-9}$ from the cosmological constant to $10^{113}$ due to calculations in Quantum Electrodynamics (QED) and Stochastic ...
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1answer
104 views

How do you build a Lagrangian in particle/nuclear physics? (A specific example)

I know that the terms in the Lagrangian needs to be scalars (with respect to Lorentz symmetry etc.). Also I know that [see C. G. Tully (EPP) p. 85] in general, for $\psi$ in the fundamental ...
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1answer
62 views

The contraction of fermion field in 1+1-dimensional massless QED

My question comes from the textbook by Peskin & Schroeder, the integral (19.26): $$\begin{align} \int \frac{d^2 k}{(2\pi)^2}\! e^{- i k\cdot (y-z)}\frac{i \not{k}}{k^2} = -\not\partial ...
2
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1answer
57 views

Why are Green Functions/(Correlation Functions) not on the mass shell?

The difference between Green Functions and the S-matrix in Quantum Field Theory is whether the momentum is on the mass shell. Why are the Green Functions/(Correlation Functions) not on the mass shell? ...
3
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1answer
72 views

Question about surface term in QFT problem

I am trying to follow the solution of the following problem (Srednicki 39.2): To show that: $$J_z b_s^\dagger(p\hat z)|0\rangle=\frac{1}{2}\ s\ b_s^\dagger(p\hat z)\ |0\rangle, $$ where $J_z$ ...
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1answer
41 views

Ladder operators evolution for fermions

For the free Dirac field we have $$ \psi(x) = \sum_s\int d\Omega_{m}\frac{1}{\sqrt{2}k_0}\left(b(\mathbf{k},s)u(\mathbf{k},s)e^{-ik\cdot x}+d^\dagger(\mathbf{k},s)v(\mathbf{k},s)e^{+ik\cdot ...
2
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1answer
52 views

Transformation of the scalar field under Lorentz Boost [closed]

Assume a Lorentz transformation $\Lambda$ is to be implemented as the unitary operator $U(\Lambda)$ in the Hilbert space of quantum states of the Fock representation upon which the scalar Klein-Gordon ...
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0answers
37 views

If 2 photons collided head on, what would happen? [duplicate]

If 2 photons, in perfect synch (frequency, amplitude, etc. were all equal) and they collided head on, what would happen? Would they pass right through each other? Would they interfere, then go back to ...
4
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1answer
167 views

A question about the energy of turning on and off interaction adiabatically in QFT

I read a saying as follows: In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
0
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1answer
91 views

Eigenstates of a bosonic field operator

Even though related questions are discussed here and here, I am still confused about the eigenstates of the field operator of a bosonic field $$ ...
2
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1answer
203 views

Mølller scattering

I came across Mølller scattering today (which is just a fancy name for electron-electron scattering. I'm confused as to why there are two tree level Feynman diagrams for this process: Check out the ...
0
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1answer
56 views

Field transformations

I'm reading Maggiore's book "A modern introduction to quantum field theory" and I'm very confused by what he did in chapter 2.6 page 31 eq. (2.80). He basically wants to find the generators of the ...
8
votes
1answer
251 views

Why are non-Abelian gauge theories Lorentz invariant quantum mechanically?

I seem to be missing something regarding why Yang-Mills theories are Lorentz invariant quantum mechanically. Start by considering QED. If we just study the physics of a massless $U(1)$ gauge field ...
5
votes
1answer
191 views

S-Matrix and normalization of states

I'm trying to understand what is the S-matrix in QFT. People say that it has to be a unitary matrix, but that I guess will change with a different normalization of the incoming and outgoing states. My ...
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0answers
33 views

Example of critical (non-relativistic) quantum field theory in 1D?

Is there an example of a critical non-relativistic bosonic quantum field theory in 1D (no time)? So, the field theory can be describe by annihilation, $\psi(x)$, and creation operators, ...
4
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1answer
68 views

How can we measure chirality in experiments?

Chirality is a concept quite different from helicity. These two concepts only happen to have the same numerical value for massless particles. I understand that we can measure helicity, but how can we ...
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1answer
33 views

Sphaleron interactions erase baryon asymmetry?

The sphaleron interactions in the standard model is $(B-L)$ conserving and $(B+L)$ violating. Each sphaleron transition causes $\Delta B$ and $\Delta L$ to change by the same amount so that ...
13
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1answer
436 views

Suggested reading for quantum field theory in curved spacetime

I want to learn some QFT in curved spacetime. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT ...
3
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0answers
32 views

Trilinear term in SUSY soft-breaking

In MSSM soft-SUSY breaking, there are such term called 'A-triliear term'. But, some papers, e.g Riva-Biggio-Pomarol, do not have trilinear term. What is the use of introducing trilinear term?
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2answers
61 views

Logarithmic discretization in Anderson´s model

Is there some motivation for the construction of Ladder operator that compound the recursive halmitonian of the Anderson model for numerical renormalization contained is this paper?