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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276 views

Do exact beta functions exist in (super)gravity theories and string theory?

An exact beta function exists for Super-Yang-Mills theories in 4D without matter - the so-called NSVZ beta function. Does a similar exact beta-function exist in gravity or supergravity theories? In ...
5
votes
0answers
111 views

Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
1
vote
1answer
291 views

Feynman Diagram in $\phi^3$ theory

I'm slightly befuddled by is what it means when I'm asked to Draw the Feynman diagram in momentum space for the two point function of $\frac{\lambda}{3!}\phi^3$ theory for order $O(\lambda^2).$ ...
5
votes
1answer
229 views

Quantum field theory meson scattering calculation (scalar yukawa theory)

Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson ...
2
votes
1answer
153 views

Commutation Relations for Creation & Annihilation Opertors of Two Different Scalar Fields

Let us consider two different scalar fields $\phi$ and $\chi$. The commutation relations for the creation and annihilation operators of the scalar field $\phi$ are given by $$ [a(\textbf{k}), ...
2
votes
0answers
94 views

Feynman rules of a theory in non-standard form

I am currently studying lecture notes by Akhmedov on interacting scalar field theory in de Sitter space. In these notes, he considers a scalar field theory of the form ...
31
votes
9answers
21k views

Is anti-matter matter going backwards in time?

Or: can it be proved that anti-matter definitely is nót matter going backwards in time? From wikipedia: There is considerable speculation as to why the observable universe is apparently almost ...
5
votes
1answer
389 views

A question about Feynman diagram and symmetry factor

Consider a $\varphi^3$ theory: $$ Z_1(J) \propto \exp\left[\frac{i}{6} Z_g g\int \mathrm{d}^4 x \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right] Z_0(J), $$ where $$ Z_0(J) = ...
1
vote
1answer
72 views

$\mathrm{d} \Omega_{CM}$ for a $1\rightarrow 2$ particle decay?

The differential solid angle is described in e.g. Srednicki's QFT text but only for the case of scattering. Because in the case of scattering it's defined with respect to the incoming three-momentum ...
4
votes
1answer
133 views

Feynman graphs of Compton scattering

Compton scattering is usually described two Feynman graphs (in the second-order perturbative expansion of scattering matrix) that can be described in the following way: annihilation of a ...
11
votes
1answer
330 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 ...
0
votes
0answers
32 views

What does the notion of basis sets for photons in number of particle picture?

Since $$|n.\rangle=|u_{k_1}\rangle\otimes...\otimes|u_{k_1}\rangle\otimes|u_{k_2}\rangle\otimes...\otimes|u_{k_2}\rangle\otimes...\otimes|u_{k_m}\rangle\otimes...\otimes|u_{k_m}\rangle$$(There are ...
5
votes
0answers
136 views

Casimir Forces and its associated Feynman Propagator

This is a continuation to my previous question, in which I began an attempt solve the Casimir Force problem using path integrals. As one of the answers there suggest I solve the Feynman propagator ...
5
votes
3answers
290 views

Extending General Relativity with Kahler Manifolds?

Standard general relativity is based on Riemannian manifolds. However, the simplest extension of Riemannian manifolds seems to be Kahler manifolds, which have a complex (hermitian) structure, a ...
4
votes
1answer
162 views

A question about causality and Quantum Field Theory from improper Lorentz transformation

Related post Causality and Quantum Field Theory In Peskin and Schroeder's QFT p28, the authors tried to show causality is preserved in scalar field theory. Consider commutator $$ [ \phi(x), \phi(y) ...
7
votes
2answers
181 views

No monopoles in the Weinberg-Salam model

I'm reading Chapter 10.4 on the 't Hooft-Polyakov monopoles in Ryder's Quantum Field Theory. On page 412 he explains why magnetic monopoles cannot appear in the Weinberg-Salam model. I'm I right by ...
0
votes
2answers
158 views

Which one is correct Dirac equation?

For a particle in potential $U(x)$ in 1D which equation is correct $$i\hbar\frac{\partial\psi}{\partial t}=(cp \sigma_x+mc^2\sigma_z+U(x))\psi$$ or $$i\hbar\frac{\partial\psi}{\partial t}=(cp ...
1
vote
2answers
307 views

Reeh–Schlieder theorem in QFT and entanglement in biological systems

Context: There have been a few papers out recently which mention how photosynthesis in plants might have connections to entanglement, or even perhaps that entanglement is causing photosynthetic ...
13
votes
1answer
298 views

Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold

In Witten's paper Quantum Field Theory and the Jones Polynomial, he mentioned that: Geometers have long known that (via de Rham theory) the self-dual and anti-self-dual Maxwell equations are ...
1
vote
0answers
86 views

Quantum tunneling in a time dependent potential

I wonder if I could use the technique for finding the tunneling rate given by $$ \Gamma=2 \Im[ F]$$ where $F$ is the free energy in case of time dependent potentials? Relevant to the previous ...
-3
votes
1answer
129 views

are sub-atomic particles really particles or mere concepts in our minds? [closed]

are sub-atomic particles really particles or mere concepts in our minds? do they exist independently of human thought? In the tenth century, Ibn al-Haytham initiated the view that light proceeds ...
-1
votes
1answer
158 views

How is the current for the Dirac equation derived?

Why is it that the derivative of the current $j^\mu$ is the difference between the Dirac equation and its adjoint?
4
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1answer
295 views

Components of the Weyl spinor field

In the Weyl basis we can separate the spinor field into 2 components: the right-chiral spinor and the left-chiral spinor. Each of these fields has again 2 components which are coupled. What is the ...
3
votes
0answers
41 views

Recommendation: Advanced topics in quantum field theory [duplicate]

I have read Srednicki's Quantum Field Theory book. I want to learn more about advanced topics in field theory, such as geometry and topology in field theory, topology defect, anomaly, soliton, ...
0
votes
3answers
119 views

Duality behavior of light and effect of system scale on its behavior [closed]

Does an electromagnetic wave that makes by antenna behaves purely as wave for all the times? or it can change its behavior as photon? and does the scale of system effect on behaving as EM wave or ...
6
votes
0answers
106 views

Is the Higgs bare mass larger than the physical mass?

The Higgs boson propagator can be written $$\frac{1}{p^2-m^2+\Sigma(p^2)}$$. If we take $p^2=m_P^2$ the physical mass, we get $m_P^2=m^2-\Sigma(m_P^2)$. Now, if $\Sigma\sim \Lambda^2$, we get ...
8
votes
1answer
115 views

About the recent discovery of tetraquark boundstates

I am referring to this, http://home.web.cern.ch/about/updates/2014/04/lhcb-confirms-existence-exotic-hadron So how does this work if we stick to keeping quarks in the 3 dimensional fundamental ...
4
votes
1answer
330 views

Mandelstam variables 1 positive 2 negative

The three Mandelstam-variables are defined as: $$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the ...
2
votes
0answers
49 views

Optical Theorem ,how can experiment distinguish the unscattered wave from the forward scattered wave?

How can experiment distinguish the unscattered wave from the forward scattered wave? The Optical Theorem says the imaginary part of the forward wave determines the cross section for an initial ...
2
votes
0answers
41 views

Definition of the Effective Particle

We define the effective particle creation and annihilation operators which are collectively and commonly denoted by $\hat{q}_s$: $$\hat{q}_s := \hat{U}_s \, \hat{q}_0 \, \hat{U}^\dagger_s $$ where ...
2
votes
1answer
55 views

Unit determinant for relevant symmetry groups in QFT

When treating QFT we want our theory to be invariant under different symmetry groups, for example, the Standard Model is a non-abelian gauge theory with the symmetry group $U(1)×SU(2)×SU(3)$. ...
9
votes
1answer
190 views

A graphical proof that the $SU(2)/\mathbb{Z}_2$ vortex is non-orientable

The text, see [1], compares the vortex solutions of a spontaneously broken symmetry $U(1) \rightarrow 1$ and $SU(2)\rightarrow U(1) \rightarrow \mathbb{Z}_2$. The vortices can be classified by ...
17
votes
2answers
512 views

S-Matrix in $\mathcal{N}=4$ Super-Yang Mills

This is a general question, but what is meant when people refer to the S-Matrix of $\mathcal{N}=4$ Super Yang Mills? The way I understood it is the S-Matrix is only well defined for theories with a ...
5
votes
0answers
82 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...
2
votes
2answers
77 views

Gauge symmetry for p-forms

It is well known that the Lorentz invariance of the S-matrix implies Gauge redundancy for 1-forms,'photons'. Does this argument go through to p-forms? That is does lorentz invariance of s-matrix of ...
4
votes
1answer
128 views

Gravitational Chern-Simons theory for bosons and fermions

Q1: What is the difference of boson and fermions for their Gravitational Chern-Simons theory? I suppose in general if the metric is not flat, we have vierbein ${e_{\hat{b}}}^{\nu}$, with $$ ...
7
votes
1answer
126 views

A question about a complex integration in Peskin's QFT textbook

In page 27 (2.52), the integration is $$\int_{-\infty}^{\infty}dp \frac{p e^{ipr}}{\sqrt{p^2+m^2}}$$ He says that there are two branch cuts starting from $\pm im$ But I learn in complex analysis ...
3
votes
1answer
475 views

Formula for Symmetry Factor

In $\phi^3$ theory, are there any formula for determining the Symmetry factor as that is found for the $\phi^4$ theory in any standard book of Quantum Field Theory?
5
votes
3answers
343 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
4
votes
1answer
140 views

Derivation of matrix element

I have tried to understand paragraph 10.7 (Kallen-Lehmann Representation) in Weinberg's Quantum theory of fields (vol.1). He calculated matrix element $$\langle0|\Phi(0)|p\rangle ...
15
votes
2answers
2k views

Self energy, 1PI, and tadpoles

I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be ...
2
votes
0answers
73 views

A question on IR cancellation caculation in peskin schroeder

In Peskin and Schroeder Introduction to Quantum Field Theory book, above equation 6.64 on pg. 200, it was said that "to gain better understanding, of the divergence, let us evaluate the coefficient of ...
5
votes
1answer
120 views

Why is the Yang-Mills Comparator unitary?

In chapter 15.2 of Peskin, the comparator is defined, as some object $U\left(y,\,x\right)$ which transforms as: $$ U\left(y,\,x\right) \mapsto V\left(y\right) U\left(y,\,x\right) ...
2
votes
1answer
211 views

Equations of motion for the Yang-Mills $SU(2)$ theory

I have an exercise for Yang-Mills theory. I can't find answer anywhere. Derive equations of motion for the Yang-Mills theory with the gauge group $SU(2)$ interacting with $SU(2)$ doublet of scalar ...
0
votes
3answers
156 views

Is Space-Time a special form of energy?

I know space-time can be influenced by matter and energy, so it must be somehow mingled in with the mix of it all, but does space-time have a fundamental particle? Can we make a little bit of ...
14
votes
2answers
284 views

Infrared-free QED and Higgsless standard model phenomenology

This is one of those "what if" fantasy world type questions. I like hard sci-fi so please no "well, you changed one thing about the world so now anything goes." :) What if the Higgs had no vev? That ...
6
votes
1answer
470 views

energy momentum tensor and covariant derivative

In field theory, the energy momentum defined as the functional derivative wrt the metric $T_{\mu\nu}=\frac{2}{\sqrt{-g}}\frac{\delta S}{\delta g^{\mu\nu}}$ (up to a sign depending on ...
2
votes
1answer
80 views

Can symmetry generators anticommute with the S-matrix?

In Coleman and Mandula's proof of the Coleman-Mandula theorem, they define a symmetry transformation as an unitary $U$ which, turns one-particle states into one-particle states, acts on ...
2
votes
2answers
109 views

Electron Electric Field Mass?

I am confused of whether or not the expected electromagnetic field generated by the point-like electric charge of the electron distributed smoothly across space as a probability distribution creates ...
5
votes
2answers
121 views

Defining quantum effective action (Legendre transformation), existence of inverse (field - source)?

Given a Quantum field theory, for a scalar field $\phi$ with generic Action $S[\phi]$, we have the generating functional $$Z[J] = e^{iW[J]} = \frac{\int \mathcal{D}\phi e^{i(S[\phi]+\int d^4x ...