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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Anomalies in QFT books

Why in most QFT books when author discusses of non-invariance of measure of path integral (massless fermions interact with gauge fields) $$ \int D\bar{\Psi} D\Psi \to |\Psi \to U\Psi , \quad ...
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46 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 ...
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27 views

Invisible stars due to finite photons [duplicate]

When we study black body radiation, we often make calculations assuming a continuum of radiation with some amount of flux. In reality, there is a very very large number of photons being emit per unit ...
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1answer
57 views

When is quantum optics “correct”?

What is the regime under which we may consider quantum optics description of light a good approximation of a more correct theory such as QED? By quantum optics I mean describing the electromagnetic ...
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51 views

Level quantization of 7d $SO(N)$ Chern-Simons action

In 3d, one can write down the $SO(N)$ Chern-Simons action to be $$S(A)=\frac{k}{192\pi}\int_{M}\text{Tr}(A d A +\frac{2}{3}A^3),$$ where $A$ is an $SO(N)$ connection. The level quantization can be ...
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36 views

Typical form of the beta function of the renormalization group

Why in "typical" cases (according to some non-English text I read), does the $\beta$-function have the form $$ \beta (g) = ag^{2} + bg^{3} + O(g^{4})\ ? $$ I.e., why are there no linear or logarithmic ...
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95 views

Complex integration by shifting the contour [migrated]

In section 12.11 of Jackson's Classical Electrodynamics, he evaluates an integral involved in the Green function solution to the 4-potential wave equation. Here it is: $\int_{-\infty}^\infty dk_0 ...
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141 views

Determine if Theory is Unitary from Lagrangian

Question: Given a quantum theory specified with a Lagrangian and the degrees of freedom to be varied, what is the procedure to determine if the theory is unitary or not? Concrete example to aid ...
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31 views

Mapping Issues with Unbounded Operators

Consider the operator-valued generalized function $\phi^{(k)}_{l}:=\phi^{(k)}_{l}$ on space-time $\mathcal{M}$. Now, smooth the operator-valued generalized function with test function $f(x)$ ...
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4answers
116 views

Nature of Fields in QFT

I'm not exactly an expert in quantum physics, but this seems to be a simple question, and I can't find an answer anywhere! There are specific types of fields used in physics: scalar fields (i.e. as ...
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35 views

How to derive the scale factor for special conformal transformation? [on hold]

By definition a conformal transformation of the coordinates is an invertible mapping $x\rightarrow x'$ which leaves the metric invariant upto a scale factor: \begin{equation} g_{\mu\nu}'(x') = ...
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88 views

Mathematical Prerequisites for QFT [on hold]

I am curious about which areas of mathematics one should be comfortable with before learning QFT. I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to ...
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17 views

Collisional energy loss in static QGP

Why is collisional energy loss in static QCD medium equal to zero?
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1answer
51 views

Ambiguous points in spontaneous symmetry breaking of discrete symmetry

For a discrete symmetry: At the minimum value of the potential, $V$, in the Lagrangian density, why do we take $\phi= \langle v\rangle + \eta$? Aren't we deliberately breaking the symmetry? If we ...
2
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1answer
67 views

How does string theory describe classical gravity theory, and QFT? [closed]

I am learning string theory, as I understand, gravitons exist as modes in string excitations, and also other particles. It gave me this picture: a lot of strings fulling in the spacetime, excitations ...
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2answers
65 views

Is it possible to create matter from space?

Like could maybe fluctuate the space some how and make the virtual paricles turn into normal matter
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48 views

What's the value of the coupling constant in interacting field theories?

Consider this Lagrangian : $L = \frac{1}{2}(\partial_\mu \Phi)^2 - \frac{M^2}{2}\Phi^2 +\frac{1}{2}(\partial_\mu \phi)^2 -\frac{m^2}{2} \phi^2 -\mu\Phi\phi^2$ Its interaction term is given by : ...
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1answer
64 views

Moduli spaces in string theory vs. soliton theory

In both string theory and soliton theory, moduli spaces are frequently used. As far as I known, for soliton theory, moduli spaces are something like collective coordinates for solitons, and for ...
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1answer
30 views

Difference between Veneziano amplitude and Virasoro shapiro amplitude

I have been study about Veneziano amplitude and Virasoro Shapiro amplitude. I want to summarize this two amplitude in the following way, please check that i am understand them properly. Veneziano ...
2
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1answer
67 views

change of variable in a 2-loop integral

given the 2 loop integral $$ \int dq_{1} \int dq_{2}F(q1,q2) $$ (1) then in dimension D=4 our integral will be a 8-dimensional integral so why can not make a change of variable to 8-dimensional ...
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2answers
85 views

Does one really need classical physics in order to understand quantum physics? [closed]

I want to start studying quantum mechanics, and then move to quantum field theory. I have a strong mathematical background, and I think this aspect of quantum physics won't be a problem to me. Though, ...
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2answers
92 views

Lorentz symmetry and Noether's theorem

I'm trying to overcome some misunderstanding that I have in Noether's theorem. There is formula in David Gross's Lectures on QFT for Noether's theorem: ...
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1answer
93 views

In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator ...
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2answers
103 views

LHC data and mathematics of QFT

I'm reading Frederic's Paugam Towards the Mathematics of Quantum Field Theory, an advanced theoretical physics book. I would like to know how I could apply the theories in this book. For example, ...
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2answers
68 views

Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \begin{equation} \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta ...
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72 views

An electron is an excitation of the electron field. So when we observe a higgs boson that means we've excited the higgs field?

See this related question: If particles are excitations what are their fields? I ask this question because, according to a lecture, the higgs boson was frozen into a "matrix" at some point before ...
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1answer
159 views

Fundamental representation in quantum field theory

In QFT we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to the ...
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60 views

Understanding the effective low-energy Lagrangian for hadrons

My course in Higgs Physics is discussing a two-nucleon low-energy effective theory of hadron interaction. With $\psi=(p,n)$, the pion is defined as $\vec{\pi}= i \bar{\psi}\vec{\tau} \gamma_5 ...
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25 views

Atomic Brownian Motion

Since atoms 'wiggle' proportionally to their energy level, I have two questions: Does it last 'forever'? Absolute Zero question And so, is this 'flux' a fundamental force? Then as an extra ...
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2answers
72 views

What is the reason for the $ i \tau_2 $ - factor in the higgs coupling with up-type quarks?

The quark mass term in the Standard Model Lagrangian looks like this: $$ L = - \lambda_d \bar{Q}\phi d_R - \lambda_u \bar{Q} i \tau_2 \phi^* u_R $$ What is the reason for the $ i \tau_2 $ - ...
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1answer
44 views

Why does the state space contain states with negative norm and what would be an example?

My lecture script of Quantum Field Theory states that " the state space contains states with negative norm ". Why does it have to be like this and what would be an example fo such a state?
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2answers
262 views

For a particle to have physical mass, is it always necessary to have a mass term in the lagrangian?

Since the self-energy adds to the bare mass defined in the Lagrangian, is it possible to create a physical particle mass from the self-energy alone, with no mass terms occuring in the Lagrangian? On ...
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1answer
82 views

Why doesn't the photon have mass? The Higgs mechanism and pre-electroweak epoch

1) When electroweak separation occurred, 'why' wasn't the photon 'given' mass like the W and Z bosons? i.e why don't photos interact with the higg's field? 2a) How well is the higg's mechanism ...
2
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1answer
56 views

Scalar Particles, Flavor Changing Processes and Gauge Symmetries

Let's consider an extended version of the Standard Model (SM) with a new Yukawa operator of the form $$ \sum_\ell g_\ell\bar{\ell}\ell \phi ,$$ where $\ell$ is any lepton of the SM and $\phi$ is a new ...
2
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1answer
74 views

Vacuum stability in quantum field theory

What exactly do people mean when they talk about the scale dependence of the effective potential ($V$)? I explain the motivation for my question (and hence my confusion) below. Please correct me as ...
2
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1answer
58 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
4
votes
2answers
60 views

Gross-Neveu model analytic solution

I need to find an analytic solution via asymptotic expansion for the following system of equations: \begin{align} & i(u_t+u_x) + v = 0 \\ & i(v_t-v_x) + u = 0 \end{align} \begin{equation} ...
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2answers
122 views

Eigenstates of a Hermitian field operator

Consider a Hermitian field operator $\phi(x)$ with eigenstates satisfying $$ \phi(x) |\alpha\rangle = \alpha(x) | \alpha \rangle $$ I'm trying to determine the inner product between the eigenstates. ...
2
votes
1answer
60 views

A Variation on Laplace's equation (context: Yang-Mills N-Instantons, Rajaraman's book)

Statement of the problem I need to solve the equation \begin{align} 0 = \frac{1}{\phi} \partial_{\sigma}\partial_{\sigma} \phi \hspace{20mm} (1) \end{align} where $\phi$ is a scalar field and ...
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0answers
21 views

Problem books like I.E. Irodov for advanced physics [duplicate]

I really enjoyed doing problems from Irodov while learning introductory physics. But I am not able to find a book like that for Graduate level physics. Can you suggest me a book which has good (and ...
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0answers
39 views

Using local U(1) Transformation to solve Problem in Path Integral [duplicate]

When we develop photon path integral, we assume that the current is always conserved. But if we consider interaction between electron/positron and photon, the Noether current is conserved only when ...
2
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2answers
74 views

Is negative mass for a bound system of two particles forbidden?

Is there any theorem that forbids the bound system of two massive particles to have negative mass?
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0answers
55 views

Hamiltonian Operator for nonrenormalizable Effective Field Theories?

Assuming we have a Effective Field Theory, for example a Real Scalar Field Theory, defined through a Lagrangian density of the form $\mathcal{L}_{eff} = \frac{1}{2}\partial_\mu\phi \partial^\mu\phi - ...
3
votes
1answer
96 views

Graph Theory and Feynman Integrals

In Vladimir A. Smirnov's book Analytic Tools for Feynman Integrals, Section 2.3, the alpha representation of general Feynman integral takes the form $$ F_{\Gamma}(q_1,\ldots,q_n;d) = ...
3
votes
1answer
134 views

Is the Higgs Boson a Force Carrier? [duplicate]

I am told there are four fundamental forces, and each of these forces has a boson that acts as its carrier. Reading this http://www.fnal.gov/pub/science/inquiring/questions/higgs_boson.html I find ...
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0answers
121 views

Propagators, path Integrals, transition amplitudes, Green's functions etc

I'm trying to make a simple conceptual map regarding some of the things in the title as they pertain to quantum mechanics and or quantum field theory, and I'm finding that I'm a little perplexed about ...
2
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2answers
134 views

Quantum Yang-Mills Theory and AdS/CFT

I just read the first chapter of Becker-Becker-Schwarz. To quote: A remarkable discovery made in the late 1990s is the exact equivalence (or duality) of conformally invariant quantum field ...
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3answers
320 views

Why is normal ordering a valid operation?

Why is normal ordering even a valid operation in the first place? I mean it can give us some nice results, but why can we do the ordering for the operators like that? Is its definition motivated by ...
2
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1answer
53 views

What is the P-parity, T-parity and C-parity of graviton? Are these conserved in general curved space-time?

I'm curious about the P,T,C-parity of graviton? 1)Are these graviton's parities even or odd? 2)Is the C,P,T-parity alternatively conserved in Einstein gravity? And does the CPT theorem still hold ...
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1answer
75 views

Operator product expansion in CFT

I'm on Polchinski's p39. Can someone please tell me the steps in the equivalence below? $$\exp\left[\frac{\alpha'}4\int d^2z_4 d^2z_5\ln|z_5-z_4|^2\frac{\delta}{\delta X^\mu(z_4,\bar ...