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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A fundamental equation for solitary wave and dimension analysis

According to the scalar Field theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$ What I want to do is ...
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64 views

How would I apply Wick's theorem to expand the time-ordered product of three quantum fields? [closed]

I think I understand how to use Wick's theorem to expand the time-ordered product of quantum fields, but I'd like to confirm that. Could you apply Wick's theorem to: ...
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1answer
114 views

What does it mean to integrate out fields from a theory?

I've done a fair bit of reading on this subject and I'm still confused about the basic principle of integrating out fields in QFT. When we have a function of 2 fields a and b, f(a,b), and we integrate ...
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1answer
53 views

What is paramagnetic current-current correlation?

I know what paramagnetism is. But first I want to know about the paramagnetic current and then the above-mentioned correlation? Actually, I am working on a paper on superconductivity where I have ...
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4answers
233 views

Physical Interpretation of the Integrand of the Feynman Path Integral

In quantum mechanics, we think of the Feynman Path Integral $\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action) as a probability amplitude (propagator) for getting from $x_1$ to ...
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1answer
115 views

Photon as the carrier of the electromagnetic force

My physics background goes as "far" as reading popsci books on QM, Particle Physics, and Cosmology so pardon my ignorance in the below questions. I've read that the photon is the particle (quanta in ...
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1answer
83 views

Comparing interaction potential in standard $ϕ^4 $theory

I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory. I have been studying about solitions so I had ...
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2answers
95 views

Dimensional Regularization involving $\epsilon^{\mu\nu\alpha\beta}$

Is it possible to dimensionally regularize an amplitude which contains the totally antisymmetric Levi-Civita tensor $\epsilon^{\mu\nu\alpha\beta}$? I don't know if it's possible to define ...
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51 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields F and D which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
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5answers
340 views

What is the path integral exactly?

I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that ...
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1answer
79 views

Transformation law for fermionic measure in functional integral

I am reading the paper "Bosonization in a Two-Dimensional Riemann-Cartan Geometry", Il Nuovo Cimento B Series 11 11 Marzo 1987, Volume 98, Issue 1, pp 25-36, ...
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77 views

Dimensional regularization and IR divergences and scale invariance

I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. Does dimensional regularization see "all" kinds of divergences? I mean - what ...
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1answer
338 views

If : V(Phi) : is nonlocal in space, does that mean interacting quantum field theory is nonlocal?

Free field theories are definitely local in . In the interaction picture, we can decompose the fields into creation operator modes and annihilation operator modes. The product of operators can be ...
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60 views

About the seesaw mechanism

I was reading about the seesaw mechanism in my Lecture notes and got a technical question. See for example http://www.lhep.unibe.ch/img/lectureslides/9_2007-11-30_SeeSawMechanism.pdf page 13. There ...
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1answer
133 views

Is the Hilbert space of $\phi^4$ theory known?

Consider free, real scalar field theory in $d=1+3$ dimensions: $H = \frac{1}{2} \partial_\mu \phi \partial^\mu \phi + \frac{1}{2} m^2 \phi^2$. The Hilbert space of this theory is known; it is just ...
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2answers
2k views

The Spectral Function in Many-Body Physics and its Relation to Quasiparticles

recently, I stumbled accross a concept which might be very helpful understanding quasiparticles and effective theories (and might shed light on an the question How to calculate the properties of ...
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1answer
124 views

Straightforward questions about calculating SUSY F-terms

So in the Lagrangian for a SUSY theory we have the F-terms, which I have seen written (e.g., in Stephen Martin's SUSY primer) as $F^*_i F^i$ where $F^i = \frac{\partial W}{\partial \phi^i}$. I ...
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56 views

How does one write eigenstates of field operators in terms of particle states in scalar field theory?

I am reading the first paper in Schwinger's QED anthology, where he discusses his action principle. In this, he writes down states that are simultaneous eigenkets of the field operators at all points ...
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201 views

Second quantization

In second quantization we use Hamiltonian in form: $$H=\int d^3x [ \psi^{\dagger}(x) h \psi(x)],$$ where $h$ is Hamiltonian density. The field operators have following form: $$\psi = \sum\limits _{i} ...
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1answer
432 views

Interaction potential in standard $\phi^4$ theory

In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by $$S=\int d^d\! x ...
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1answer
110 views

Lorentz invariance of positive energy solutions to the Klein-Gordon equation

I am reading Arthur Jaffe's Introduction to Quantum Field Theory. (You can find it here.) There is an interesting question posed in Exercise 2.5.1: Solutions to the Klein-Gordon equation propagate ...
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1answer
100 views

Why is $R^2$ gravity not unitary?

I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity? My naive ...
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7answers
616 views

Is there a symmetry associated to the conservation of information?

Conservation of information seems to be a deep physical principle. For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory. We may wonder if there is an underlying ...
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1answer
68 views

Are observables associated to spacetime regions?

In the Haag-Kastler approach to axiomatic quantum field theory, it is assumed that observables are 'associated' to spacetime regions. What this actually means is that there is a map $\mathcal{A}: R ...
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66 views

Coupling constant problem

In the scalar $φ^4$ theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}(\partial_t\phi)^2 -\frac{1}{2}\delta^{ij}\partial_i\phi\partial_j\phi - \frac{1}{2}m^2\phi^2-\frac{g}{4!}\phi^4. $$ I want ...
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118 views

How does Haldane conjecture follow from the topological $\Theta$ term

The one dimensional SU(2) Heisenberg quantum spin chain is known to be described by the 1+1d O(3) nonlinear $\sigma$ model with a $\Theta$ term, following the action ...
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55 views

No mixing in light cone perturbation theory

In hep-ph/0609090, Triumvirate of Running Couplings in Small-x Evolution, Kovchegov et. al. calculated the running coupling correction to the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and ...
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1answer
469 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 ...
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1answer
260 views

Symmetries in Wilsonian RG

I wanted to know if there is a theorem that in writing a Lagrangian if one missed out a term which preserves the (Lie?) symmetry of the other terms and is also marginal then that will necessarily be ...
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1answer
94 views

Symmetries in Wilsonian RG (2)

This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG In the liked paper why do the equalities in equation ...
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1answer
135 views

$\phi ^4$ theory explaining [closed]

In $φ^4$ theory we often write the Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$ If I want to write from the ...
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600 views

What are the various physical mechanisms for energy transfer to the photon during blackbody emission?

By conservation of energy, the solid is left in a lower energy state following emission of a photon. Clearly absorption and emission balance at thermal equilibrium, however, thermodynamic equilibrium ...
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3answers
335 views

How Uncertainty Principle, Vacumm fluctuations and Energy Conservation coexist in QFT?

Recently I had a debate about the uncertainty principle in QFT that made me even more confused.. Because we use Furrier transforms in QFT we should have an analogue to the usual Heisenberg ...
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1answer
52 views

Given expectation values for E and B, can you find an associated state?

When we quantize the electromagnetic field, we develop the concept of the field operator $A(\vec{r},t)$ and the simultaneous eigenstates of momentum and the free field Hamiltonian (i.e., each ...
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2answers
217 views

Can scattering amplitudes be simplified with 1PI diagrams?

I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
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57 views

Light Front Dynamics and Infinite Momentum Frame

What is the the relationship between Light Front Dynamics (One of the forms of dynamics pioneered by Dirac), and the infinite momentum frame? In the literature, it is claimed that the two are very ...
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91 views

Mirror Matter Hypothesis?

What is the current state of the hypothesis of mirror matter today? Are there any experimental data or theoretical arguments that exclude it by now, or is it still considered viable among physicists? ...
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59 views

Contact Term and Schwinger Term

In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'. When deriving the quantum equations of motion for time-ordered ...
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1answer
39 views

Higgs VEV in terms of measurements on an ensemble?

Let $A$ be a Hermitian operator corresponding to some observable. If we prepare $N$ identical systems in the state $\psi$ and measure this observable in each system, the average of the measurements ...
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69 views

Noether currents for the BRST tranformation of Yang-Mills fields

The Lagrangian of the Yang-Mills fields is given by $$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ ...
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8answers
594 views

Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories. So why is it that it's popular ...
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99 views

Quantum Electrodynamics

I was wondering if anyone could give a simple explanation of how light interacts with matter. From what I have read in QED, electrons will repel each other because of their ability to emit and ...
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0answers
38 views

CP-symmetry and Ward identities and finite temperature

I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature. Wikipedia states about Ward-identities: The ...
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40 views

Lagrangians for non-local equations of motion

Say I have a multicomponent field $X_a(x,t)$ such that I know it Fourier modes satisfy the following equation of motion, $(\delta_{ab} \partial_t + \Omega_{ab}(t))X_b(k,t) = e^t \int \frac{d^3p ...
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0answers
96 views

exercise books for Feynman diagrams [duplicate]

I know QFT at graduate level but I'll like to master the skill of working with Feynman diagrams. I'm looking for a book of solved exercises on this topic. Specifically, I'm looking for the kind of ...
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1answer
261 views

About the definition/motivation/properties of the twisted chiral superfield in ${\cal N}=2$ theories in $1+1$ dimensions

The following is in the context of the ${\cal N}=2$ supersymmetry in $1+1$ dimensions - which is probably generically constructed as a reduction from the ${\cal N}=1$ case in $3+1$ dimensions. In ...
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1answer
167 views

Calculation of Commutation in constraint analysis

During analysis the constraint from a theory, suppose my canonical Hamiltonian is $$H_c=P^A\dot{A}+P^B\dot{B}-L$$ where $P^A=\frac{\partial L}{\partial \dot A}$ and $P^B=\frac{\partial L}{\partial ...
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3answers
702 views

No hair theorem for black holes and the baryon number

The no hair theorem says that a black hole can be characterized by a small number of parameters that are visible from distance - mass, angular momentum and electric charge. For me it is puzzling why ...
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2answers
348 views

Gauge invariance and diffeomorphism invariance in Chern-Simons theory

I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to ...
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1answer
83 views

Density operator in second quantization

I would want to understand why the density operator in second quantization takes the form: $$\rho_\sigma(\mathbf{r})=\Psi_\sigma^\dagger(\mathbf{r})\Psi_\sigma(\mathbf{r})?$$ Is this a definition or ...

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