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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total cross section and contribution

Since in electron electron scattering if initial energy is quite large then muon antimuon production process can also take place which also contributes thus increases the total cross section. What ...
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138 views

Quantum field theory's completeness

I realize Quantum Field Theory doesn't include gravity at all. Other than that, does QFT completely describe all electromagnetic and nuclear interactions? In other words, does it describe (at least) ...
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176 views

The state of Indefinite metric in Quantum Electrodynamics

I faced difficulties to grasp why indefinite metric is introduced from no where in QED, after searching internet I found that this is a problem in QED, because one needs it to preserve theory's ...
2
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1answer
104 views

Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
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174 views

Why isn't Quantum Yang-Mills Rigorous?

Obviously one of the major components of the Yang-Mills existence and mass gap problem of the Clay institute is the proof that 3+1d quantum yang-mills theory has rigorous foundations. This (I believe) ...
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88 views

Anyons: Effect of braiding on fusion multiplicities

In the theory of non-abelian anyons, essential information is stored in the fusion multiplicities or Verlinde coefficients $N_{ab}^c$. Having the Pants Decomposition in mind, it is possible to use ...
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72 views

How does determinism manifest out of QFT?

Classical electrodynamics is deterministic. QED is indeterministic, or probabilistically random. Yet they agree with each other? What am I missing?
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61 views

How to cancel infinite mass corrections for quantities without counterterms?

I'm trying to understand how infinite mass corrections are cancelled for a particle that is massless at tree level. In short the problem is that we have infinite diagrams, but we don't have a ...
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96 views

Entanglement in single particle state

Is it possible that we have entanglement in different degrees of freedom of a singe particle. like spin and linear momentum .
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190 views

In what sense do Goldstone bosons live in the coset?

Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. ...
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107 views

Calculating Tr(log($\Delta_F$))

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = ...
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578 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, ...
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53 views

Symmetry factor of $n$-point one-loop diagram [duplicate]

If we have a one-loop diagram in $\phi ^ 3$ scalar field theory with $n$ external lines, then what is its symmetry factor? I have drawn the diagram I am looking for, but instead of $6$ external ...
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98 views

Yang-Mills existence and mass gap

In the Clay institute problem description of the Yang-Mills existence and mass gap problem it states that the quantum Yang Mills needs to be formulated in $\mathbb{R}^4$ space. I was wondering whether ...
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58 views

Pedagogical projects in QFT for self-study purposes? [closed]

I'm reading Srednicki's QFT textbook. I'd like to do some projects that put the content learned into actual use. Is there any good project topic? I don't mind if it's already worked out some where. ...
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109 views

Duality between Euclidean time and finite temperature, QFT and quantum gravity, and AdS/CFT

The thoughts below have occurred to me, several years ago (since 200x), again and again, since I learn quantum field theory(QFT) and statistical mechanics, and later AdS/CFT. It is about the duality ...
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91 views

Self-adjointness

I know I have posted this question before some time ago. But no one could help so I decided to put my problem in another background. The Schrödinger equation of a free scalar field is given by ...
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1answer
402 views

What is the meaning of Non-Relativistic theory in Condensed Matter Physics?

I an attempt to evade the Goldstone Theorem, it is argued in Gilbert and Klein and Lee's paper that in a non-relativistic field there exists a preferred direction which can be used to evade ...
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77 views

Symmetry factor of Feynman diagram

What is the symmetry factor for the following Feynman diagram if we assume that the external points are held fixed? Please ignore the arrows in the diagram. I am referring to the second diagram on ...
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379 views

Is an entropic force an actual force that can be explained as a fundamental interaction?

Fundamental interactions, such as electromagnetism, the strong force, the weak force, and possibly gravitation, all have something in common: They can be described in terms of relativistic quantum ...
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303 views

Different representations of the Lorentz algebra

I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
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64 views

Faddeev Popov Gauge Fixing in Electromagnetism

Reading section 9.4 in Peskin, I am wondering about the following: The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero. ...
5
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2answers
152 views

What uniquely defines a CFT?

So, I am quite new to CFT (and a as descriptive answer as possible would be appreciated). I want to know what uniquely defines a CFT in 2D and otherwise. Firstly in 2D, What defines a CFT? So I ...
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31 views

When does the correlator of a string of fields and the current vanish “sufficiently fast” at infinity and Ward's identity?

One consequence of the Ward identity (cf. Di Francesco et al) is that it means variation of correlators under infinitesimal transformation is zero. This can be seen by integrating the ward identity, ...
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278 views

How does the nature of nuclear force change between attractive or repulsive based on distance?

I know that the nuclear force is responsible for binding the protons and neutrons together in the nucleus. The force is powerfully attractive at small separations and rapidly decreases as the distance ...
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79 views

Potential of the pseudo Nambu-Goldstone boson

Pseudo Nambu-Goldstone bosons appear in breaking approximate symmetries, for instance, the QCD axions. Many literatures just write the action of those pseudoscalars without any explanation. In ...
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119 views

Energy-Momentum Tensor in QFT vs. GR

What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu ...
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99 views

Instanton in sine-Gordon equation

This is a statement from Giamarchi's book on Quantum Physics in 1D: "For a single-particle in a cosine potential, the slightest amount of tunneling between two cosine minima leads to conduction ...
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70 views

Difference between the 'phonons and virtual photons'

I understand what are virtual photons and the difference between the real and virtual photons. However, I am not able to clearly distinguish the difference between the 'phonons and virtual photons'. ...
8
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1answer
108 views

Difference between regularization and renormalization?

In my studies on quantum field theory we have come up with the concepts of regularization and renormalization. I'm a little confused about these two. In my understanding regularization is a way to ...
22
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1answer
1k views

What does it mean that there is no mathematical proof for confinement?

I see this all the time* that there still doesn't exist a mathematical proof for confinement. What does this really mean and how would a sketch of a proof look like? What I mean by that second ...
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36 views

Finite corrections to the Higgs mass in SUSY

I am worried here about specific supersymmetric scenarios in which an energy scale above the TeV is introduces. An example would be the Seesaw extension of the Minimal Supersymmetric Standard Model. ...
9
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2answers
388 views

What is the origin of the factor of $-1/4$ in the Maxwell Lagrangian?

I have seen numerous 'derivations' of the Maxwell Lagrangian, $$\mathcal{L} ~=~ -\frac{1}{4}F_{\mu \nu}F^{\mu \nu},$$ but every one has sneakily inserted a factor of $-1/4$ without explaining why. ...
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588 views

Virtual particles and physical laws

Recently, I was reading about Hawking Radiation in A Brief History of Time. It says that at no point can all the fields be zero and so there's nothing like empty space(quantum fluctuation etc.). Now, ...
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36 views

Difference between $\psi_{\alpha}$ and and $u^{\pm}$ in Dirac fields?

What is clear difference between say Psi_1,psi_2,....psi_4 and the U+- and V+- matrices in case of dirac fields or are u,v (or some book use U^(1),U^(2)) matrices some rep of the same
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117 views

What is the concept of cosmic strings?

What is the concept of cosmic strings? Is it related to the strings in the string theory, and if it is, then how?
5
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67 views

Parity on gamma matrices

I want to understand clearly why $ P \gamma^{\mu} P = \gamma^{\mu} $, where $ P $ is the parity operator. This result follow for example from pag. 66 of Peskin-Schroeder. The parity operator acts ...
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1answer
223 views

Seiberg-Witten theory and Superconductivity

There seems to have some (deep) relation between Seiberg-Witten theory and superconductivity. e.g. this Witten paper. Q: Could someone introduce the relations between the twos both physically in ...
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1answer
99 views

Is the total cross section a Lorentz Invariant?

In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely: $$ {1 \over E_{A} E_{B} |v_A - ...
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1answer
62 views

Under what conditions is a vector-spinor gamma trace free

I came upon the concept of irreducible vector-spinors while trying to simplify an expression involving the gravitino field. It is claimed that an irredicible vector-spinor is gamma-traceless, i.e. $$ ...
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41 views

Are not the field equations proof of the holographic principle?

The field equations (e.g. Schrödinger’s/Maxwell’s) describe the four-dimensional universe as the time evolution of a three-dimensional system. This implies that the universe contains only three ...
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1answer
85 views

What are the current contenders/most promising approaches to High Tc Superconductivity?

I want to know what kinds of things theorists are currently looking at. Specifically, I want to know more about the promise that field-theoretic methods are showing. I am studying superconductivity at ...
5
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30 views

Field redefinitions and new counterterms

My question was motivated by my attempt to answer this question. Suppose we are given an action and we make a change of variables such that the theory is non-renormalizable. Does the new theory then ...
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1answer
63 views

Matsubara Frequencie

I have to evaluate the following Matsubara sum: $$\frac1\beta \sum \left(\omega^2 +a^2\right)^{-1}$$ for Bosonic-Matsubara frequencies. I know contour integration it the way to go. Therefore, I ...
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2answers
122 views

Why gauge $SU(N)$ and not $SO(N)$?

When building models people typically gauge $SU(N)$ but rarely try to gauge $SO(N)$ (the only example I know about is $SO(10)$, but even that isn't quite $SO(10)$ but actually its double cover). At ...
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9answers
2k views

Is a “third quantization” possible?

Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
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39 views

Spin matrix for various spacetime fields

Let $V^{\mu}$ be a vector field defined in a Minkowski spacetime and suppose it transforms under a Lorentz transformation $V'^{\mu} = \Lambda^{\mu}_{\,\,\,\nu}V^{\nu}$. We can write this like ...
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833 views

Virtual photons, what makes them virtual?

The wikipedia page "Force Carrier" says: The electromagnetic force can be described by the exchange of virtual photons. The virtual photon thing baffles me a little. I get that virtual particles ...
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1answer
45 views

Interchaging boson and fermion on an infinite 1 dimensional line

In 1+1 dim bosonization, one introduce the Klein factors, which are Hermitian and satisfies Clifford algebra. (1) In the case of 1 dim space is a 1D ring ($S^1$ circle), then one have left-right ...