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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No Lagrangian description v.s. No quasi-particle description

This post is aimed to stimulate some discussions. We are familiar with many physical descriptions and theories of the (many-body quantum) system, with both quasi-particle description and Lagrangian ...
4
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61 views

How to calculate gravity path integrals about an AdS background?

Suppose I have some Lagrangian of some higher derivative gravity coupled to a may be matter fields. Now I want to fluctuate it to quadratic order about an AdS background and calculate the 1-loop ...
5
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1answer
474 views

Is it really impossible to calculate in advance the result of throwing dice?

Is it really impossible to calculate in advance the result of throwing dice? After all, the physics of dice throwing is in the world of classical mechanics, rather than quantum mechanics.
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1answer
55 views

Majorana Superfields

so apologies if this is a silly question... In the type 1 see saw model we add extra Majorana fermions to our model. These fermions have to be total gauge singlets in order to have a Majorana mass ...
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41 views

Bosonization on the lattice fermion - a rigorous mapping

An inquiry: usually the bosonization is done on the field theory side. The mapping between the fermion operator to the boson operator is done for the field theory operators. As far as we know for the ...
6
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2answers
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 ...
4
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1answer
65 views

Tadpole diagram and vacuum

This statement may be well-known. For many massless theories, these tadpole diagram graphs vanish in dimensional regularization (by dimensional analysis and the absence of any inherent mass scale in ...
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0answers
28 views

Proof for the Mass gap of non-chiral Luttinger liquids with a Cosine potential

Similar to this post, I believe in condensed matter, people know the mass-gap statement for non-chiral Luttinger liquids with large $g \cos(\beta_{}^{} \cdot\phi_{})$ potential. This is the ...
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4answers
107 views

Principle of locality

Why does the principle of locality have so such great importance in physics that theory should be consistent with it?
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83 views

Deriving Feynman rules from Renormalized Lagrangian

In the context of Renormalized Pertubation Theory Peskin Schröder says: The Lagrangian $$ \mathcal{L}=\frac{1}{2} (\partial_\mu\phi_r)^2-\frac{1}{2}m^2\phi_r^2-\frac{\lambda}{4!}\phi_r^4 + \frac{1}{2} ...
5
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1answer
119 views

Derivation of neutrino oscillation phase factor

As we know, the neutrino $\nu_{\alpha}$ with flavor $\alpha=e,\mu,\tau$ is a linear combination of mass eigenstates: $$ |\nu_{\alpha}\rangle=\sum_iU_{\alpha i}|\nu_i\rangle,\quad i=1,2,3 $$ where the ...
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0answers
72 views

Proof for the Mass gap of sine-Gordon action with $g \cos(\beta \Phi)$

This is the sine-Gordon action: $$ \frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi + g \cos(\beta_{}^{} \cdot\Phi_{}) $$ ...
2
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1answer
69 views

Fierz identity with Dirac spinors

The following Fierz relation does not seem so obvious to me : \begin{equation} \bar{\psi}_1 \gamma^\mu (1+\gamma_5)\psi_2 \bar{\psi}_3 \gamma_\mu (1-\gamma_5) \psi_4 = -2 \bar{\psi}_1 (1-\gamma_5) ...
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2answers
49 views

Higgs doublet: a charged and a neutral component?

In the book 'Modern Particle Physics' byM. thomson the Higgs doublet is written as $$\phi = \left(\begin{matrix} \phi^+ \\ \phi^0 \end{matrix}\right)=\phi = \left(\begin{matrix} \phi_1 +i\phi_2 \\ ...
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0answers
43 views

O(N) sigma model renormalization

Does anyone know, is a model with lagrangian $\mathcal{L} = \frac{(\partial_{\mu}\phi_a)^2}{2}-\frac{m^2 \phi_a^2}{2}-\frac{\lambda}{8N}(\phi_a \, \phi_a)^2$ renormalizable? I'm using BPHZ scheme and ...
7
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1answer
122 views

Heuristic Motivation for Lagrangian Formalism

Does anyone know a good heuristic motivation for the Lagrangian Formalism? I think most physicist just accept at one point that it works and thats that. I think I understand the historic origin. ...
6
votes
1answer
82 views

Simplifying a seemingly simple gamma matrix identity

When studying from the book by Wise and Manohar, Heavy Quark Physics (pg 102), I came across a seemingly simple identity that I am not able to prove. It's likely an easy problem but I can't for the ...
8
votes
2answers
161 views

How do we measure meson decay constants?

I'm trying to understand how people actually measure decay constants that are discussed in meson decays. As a concrete example lets consider the pion decay constant. The amplitude for $\pi ^-$ decay ...
2
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0answers
88 views

How local fields transform in the holographic boundary

Consider a holographic description of gravity $f:\Omega \rightarrow \partial \Omega$ such that gravitational fields and curvature in a neighbourhood $\Omega$ of 4D spacetime induce local fields on ...
7
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0answers
49 views

Candidates for holographic QFT of 4D Einstein gravity

If we are to believe that holographic principle holds over a wide number of dimensions, and gravitational theories, but specially, those that are relevant to our universe, then there must be some 3D ...
4
votes
3answers
165 views

TQFT associates a category to a manifold

Any 3d TQFT (topological-quantum-field-theory) associates a number to a closed oriented 3-manifold, a vector space to a Riemann surface, a category to a circle, and a 2-category to a point. This ...
3
votes
1answer
59 views

How can a left-handed fermion field create a right-handed antifermion?

My question - which is likely stupid or appears due to some confusion - stems from the following considerations: when quantizing canonically we are told (see any book on QFT) that a Dirac fermion ...
2
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0answers
66 views

Probability density of Klein-Gordon equation

This may, perhaps, stir some healthy debate; at least I am having some "fun" thinking about it, hopefully I can solicit some outside views too. It is often regarded that the Klein-Gordon equation ...
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0answers
41 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
6
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0answers
104 views

Green's function for the inhomogenous Klein-Gordon equation

I'm trying to solve the massive Klein-Gordon equation in good old Minkowski space-time: $$(\square + m^2) \phi = \rho(t,\mathbf{x})$$ where $\square = \partial_{\mu} \partial^{\mu} = \partial_{t}^2 - ...
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1answer
40 views

Can a classical (or quantum) field, particularly the EMF, have a frame of reference?

I understand that a massless particle (such as a photon) cannot have a frame of reference. But the electromagnetic field does have mass; does it have a frame of reference? If so, I have a second ...
2
votes
1answer
107 views

NRQCD: Why are quarks and anti-quarks treated independently?

I am studying these lectures on effective field theories and I am having some problems to understand how the Non-Relativistic QCD (NRQCD) Lagrangian is constructed. This theory is often used to ...
4
votes
2answers
115 views

Stationary points of the action functional

In QFT the principle of stationary action states that we choose fields that will make the action stationary but what if the action has many stationary points? What's the significance of these other ...
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0answers
48 views

Ground State Functional and Vacuum-Vacuum Transition Amplitude

In Path Integral formalism, the vacuum-vacuum transition amplitude is defined to be (the functional integration is over all field configurations in the whole spacetime; $\Phi_{\vec{x}}(\tau)$ is the ...
5
votes
1answer
113 views

How do I deal with a quantum field in the denominator?

I am wondering how to deal with an expression like $$ \int d^4\theta \frac{1}{T + T^\dagger} \big( \dots \big) $$ If the denominator was of the form $1 + T + T^\dagger$, I could assume that $T \ll 1$ ...
1
vote
1answer
51 views

What is the leading order Feynman diagram for nucleon-anti-nucleon annihilation into two mesons ($\psi^{\dagger} \psi \to \phi\phi$)?

I am working with a standard basic scalar Yukawa theory. I.e. the only interaction term is $-g\psi^\dagger\psi\phi$, where the $\phi$ field quanta are the mesons, the $\psi$ field quanta are the ...
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votes
2answers
265 views

What's a lepto-diquark?

This questions refers to Slansky's Group theory for unified model building, page 106 of chapter 7. He assigns the weight $(1)(01)$, which is stepwise projected from $E_6$ to $SU(2)\times SU(3)$, to a ...
7
votes
1answer
262 views

Box normalization

Whenever we study free fields, the solutions of these fields (or particles, whatever feels most comfortable) are always given by plane waves. The dispersion-relation $\omega=\omega(k)$ will of course ...
2
votes
1answer
53 views

What is the generating functional for a scalar theory with two different (interacting and real) fields?

My question is specifically about how to use sources? For an interacting theory with one field, one puts a $J(x)\phi(x)$ term in the exponential in the path integral for $W[J]$. I now have two ...
5
votes
1answer
125 views

Problem understanding sign of volume integral in Minkowski space

My professor told me that a 4-dimensional Minkowski - Space Integral I was working on can be written as the product of a metric tensor and a scalar: $\int d^4 k \frac{k^\mu ...
2
votes
1answer
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?
9
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1answer
166 views

Quantization of strings, string Fock space and transition to QFT

I am not an expert of string theory and am quite uncertain about the basic ideas of string theory that I am going to ask about. I would appreciate some hints of more experienced physicists. What I am ...
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0answers
35 views

Hawking radiation at the mouth of Schwarzschild wormholes

I was researching a question for another post and it occurred to me that you might expect to see Hawking radiation at the mouth of wormholes. Given the mechanism of Hawking radiation at the event ...
1
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1answer
76 views

Euclidean functional Integrals

In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical approximation. To evaluate the ...
3
votes
1answer
86 views

How to construct an invariant Lagrangian under a Lie group $G$ generally?

How to construct an invariant Lagrangian under a Lie group $G$ generally? For example, if we have $SO(5)$'s generators which are constructed by some operators, then the question is that: is it ...
2
votes
0answers
59 views

Difference of the O(N) Non-linear Sigma model and SO(N) Non-linearSigma model

The Hamiltonian \begin{equation} H=J\sum_{i,j}\vec{n}_i\cdot\vec{n}_j \end{equation} is invariant under a global rotation $\vec{n}_i\rightarrow R\vec{n}_i$, where $\vec{n}$ is a $N$ component rotor ...
3
votes
2answers
60 views

Application of Poisson summation Formula to Casimir Effect

I'm studying the Casimir Effect at finite temperature. To calculate the Helmoltz free energy in the canonical ensemble I need to sum a particular series. In some scientific papers it is suggested to ...
2
votes
1answer
113 views

Quantum Field Theory with (2,2) metric

Does someone know some reference which treats QFT in a space with the following non-Lorentzian signature: $g_{\mu\nu}=\text{diag}(-1,-1,1,1)$. I'm interested in basic stuff like the shape of the ...
10
votes
1answer
96 views

Triality and charge

I have a few questions about triality for the representations of $SU(3)$. (I have seen the wikipedia page, but it does not make the connection with physics.) What is triality, how can you compute ...
6
votes
2answers
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 ...
7
votes
1answer
80 views

Why is the chiral symmetry $SU(2)_A$ not anomalous?

Using Fujikawa's path integral treatment of the triangle diagram, one can show that $$\mathrm{Tr} \gamma^5 = \int d^4 x\ \partial_{\mu}j^{\mu} $$ Where $j^{\mu}$ is the Noether current of $U(1)_A$. ...
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0answers
29 views

Estimation of polarization perturbative term

I'm studying a diagrammatic approach to degenerate electron gas. Now I need to prove that the energy contribution, with an arbitrary potential, of polarization at first perturbative order given by the ...
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0answers
68 views

Why is the $\theta$ term of QCD violating charge and parity (CP) symmetries?

From the non-trivial nature of the QCD vacuum, the Lagrangian is augmented with a term like \begin{equation} \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu} \end{equation} where $ ...
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votes
3answers
564 views

The path integral and Feynman diagrams

This question is somewhat of a historical one, but it also contains some physics. I am curious to find how exactly the concept of Feynman diagrams arose (I assume from Feynman's path integral)? The ...
6
votes
2answers
215 views

How to picture a quantum field?

How do we picture/imagine a quantum field ? How is it different from a classical field ? How do we picture a particle arising out of an excitation of its respective quantum field ? Please give an ...