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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Pressure and Density Using a General Lagrangian

Given a lagrangian of a form: \begin{equation}\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)\end{equation} where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
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173 views

History of the names “Feynman-gauge” & “Landau-gauge”. How arised & how settled?

Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, but could you explain the history? It's ...
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68 views

Renormalizability of standard model

I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities: The renormalizability of all of the interaction described by the Lagrangian before ...
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89 views

Massless $\lambda \phi^4$ QFT

The $\lambda \phi^4$ quantum filed theory is the textbook example (which probably cannot be constructed nonperturbatively; I'm purely interested in perturbation theory). However, usually one treats ...
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176 views

Field energy of/from virtual Photons

I have a slightly out-of line question: Consider a single electron (or it's current if you please) The STATIC ELECTROMAGNETIC field surrounding it will (no doubt) have a field energy (T) to go with. ...
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46 views

Conformal compatification of Minkowski and AdS

How do I show that the compactification of Minkowski is given by the quadric $$uv-\eta_{ij}x^{i}x^{j}=0$$ with an overall scale equivalence in the coordinates.I get that for $v \neq 0$, the surface ...
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211 views

quantum field theoretic models of decoherence

I am interested in whether there is a field theoretic description (there is, so what is it?) of the tensor product (aka density matrix) model of open quantum systems. In particular, I am interested in ...
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256 views

Why is the periodicity of fields in finite temperature QCD consequence of Trace in the action?

In finite temperature QCD, the gauge fields must be periodic in temporal direction. They say this is the consequence of trace in the action for gauge fields. How does trace imply that the fields must ...
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48 views

Ambiguity in Asymptotic Perturbative Series and Instantons

I know there are a number of questions about the asymptoticity of perturbative series and about instantons on StackExchange (e.g. Instantons and Non Perturbative Amplitudes in Gravity from user566, ...
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62 views

Angular momentum of anyons

Why is it true that anyons can have angular momentum taking any real value? Why aren't they restricted to the $j(j+1)$ integer values most are familar with?
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669 views

Why aren't all photons virtual particles even in the “vacuum” of empty space? [duplicate]

I'm thoroughly confused about the nature of electromagnetic radiation. Light is supposed to exhibit both wave and particle characteristics. But does that mean that it is both a wave and a particle or ...
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74 views

Free Field theory to Interacting Field theory

Free field theory: Why is it said that different Fourier modes in case of a free field (say, real Klein-Gordon field) are independent of each other? Interacting field theory: How exactly does the ...
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How do different fields interact with each other?

Recently I've seen a few talks and lectures about Quantum Field Theory. They explained what a "particle" means in a field, and that a large enough excitement in a certain field can excite another ...
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39 views

power counting and (superficial) non-renormalizability

Comment: This stuff is new to me so it doesn't entirely make sense (yet). Question: As I understand from Peskin and Schroeder chap 10 if you have a theory with interaction terms $\lambda \phi^n$ in ...
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128 views

Increased likelihood of photon emission due to “nearby” absorber?

Is an excited atom more likely to emit a photon if there is a similar atom in the ground state nearby ready to absorb it? When I say "nearby" I guess I mean that the absorber has an approximately ...
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214 views

Will we need to update Electrodynamics?

A contradiction to the Electrodynamics by the experiment. The author has said that, accordning to the experiment, photon is no more gauge invariant? Why is that? An important thing is that Although ...
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133 views

QFT's that have no action

What does it mean to have a QFT that can not be encoded by an action. What is by far the most powerful approach of study in such a case. What is the best studied physical theory that falls into this ...
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67 views

Ground State Energy in Euclidean Spacetime

Calculating the transition amplitude in Euclidean spacetime is useful because from it we can extract the ground state energy and ground state wave-functions values. For example, let's assume we are ...
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272 views

Why do we seek to preserve gauge symmetries after quantization?

Gauge symmetries do not give rise to conservation laws via Noether's theorem, and they represent redundancies in our description of the system. So why do we want to keep them after quantization? For ...
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388 views

Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
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59 views

A question on spin algebra

In scattering theory, one can form a lorentz invariant quantity by $\epsilon_{\mu 1 2\nu}P^{\mu}_{1}P^{\nu}_{2}$ which is really $1\otimes 1$ 's spin 0 state. Is there such a kind of argument to show ...
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2answers
91 views

Can a fundamental particle black hole with conserved charge emit Hawking radiation?

Let's says there is a fundamental particle: That is so massive that it is a black hole by itself (Compton wavelength < Schwarzschild radius) That carries a conserved quantum number (e.g. charge ...
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119 views

Black hole thermodynamics in a time dependent metric

For a time dependent space time metric, to get the thermodynamics, does the standard procedure of Wick rotating the time, and then calculating the free energy, work ?
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How exactly to show that s-matrix elements diverges because time-ordering is not well determined?

Let's have s-matrix: $$ S_{\alpha \beta} = \langle \alpha | \hat {S} | \beta \rangle , $$ $$\hat{S} = \hat{T}e^{-i\int \hat{L}(x)d^{4}x}, \quad \hat{T} \left( \hat{\Psi}(t) \hat{\Psi}(t') \right) = ...
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Young Tableau Projectors: Does the order of symmetric and anti-symmetric projectors matter?

Given a Young Tableau we find the irreducible basis of an arbitrary tensor by projecting, The projectors are usually defined as first symmetrise over the row entries and then anti-symmetrise over the ...
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Would a high energy bottom quark 'decay' to a top quark?

The reason for the long life time of $B$-hadrons is that the CKM element $|V_{tb}| > 0.999$, meaning that the preferred decay of the $b$-quark is to a $t$-quark (and vice versa). However because ...
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89 views

Why is string theory a two dimensional quantum (conformal) field theory on its worldsheet?

In string theory, we quantize the two dimensional field theory on the string's worldsheet. I have a question about this kind of quantization of string theory: did we have similar theory for point-like ...
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195 views

Normal ordering in curved spacetime

In the flat spacetime, one can perform normal-ordering to set the energy of the vacuum state to zero. I read in some places that this procedure cannot be consistently performed in the curved ...
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146 views

wave-particle duality and entanglement

By fundamental definition of a entangled system we can say that if we know the quantum state of one subsystem then we can describe the state of another subsystem. A particle possess wave-particle ...
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128 views

Rigorous QFT on a Torus

The problem description for the Yang-Mills Existence and Mass Gap problem (http://www.claymath.org/sites/default/files/yangmills.pdf) says in its "Mathematical Perspective" section that Some ...
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38 views

If non-zero cosmological constant interpreted as a repulsive filed, what would be the properties of this field's quanta?

If non-zero cosmological constant interpreted as a repulsive filed, what would be the properties of the excitation of such field, i.e. the particle which serves as the field's quantum? What would be ...
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423 views

Gauge invariance and Feynman path-integrals

Let me look at the Hamiltonian of a charged particle in a plane in a constant magnetic field ($\vec{B}$) pointing upwards - then in usual notation it is, $$\hat{H} = \frac{1}{2m}\biggl(\hat{p} + ...
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41 views

CPT symmetries for a free Klein-Gordon equation and in minimal coupling

I'm studying for an exam on relativistic quantum mechanics and one of the issues to prepare is about symmetries of Klein-Gordon equation concerning $C$, $P$, $T$ transformations for a free field, and ...
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71 views

Naive unification of scalar QFT and GR is possible?

I am thinking on the Klein-Gordon equation with curved (non-diagonal) metrics. Is it possible? Doesn't have it some inherent contradiction? If yes, what? If no, what is this combined formula?
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272 views

Time-ordering in QFT

In Srednicki QFT page 37. In the derivation of LSZ reduction formula, he introduces the time-order operator $T$, so no time-dependent creation/annihilation operators are left in the transition ...
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154 views

Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT

This maybe a very naive question. I have just started studying CFT, and I am confused by why we have two separate parts of everything in CFT (operator algebras and hilbert space), the holomorphic ...
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37 views

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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136 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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175 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 ...
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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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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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2answers
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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184 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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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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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 ...