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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Time ordering and time derivative in path integral formalism and operator formalism

In operator formalism, for example a 2-point time-ordered Green's function is defined as $\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\theta(x_1-x_2)\phi(x_1)\phi(x_2)+\theta(x_2-x_1)\phi(x_2)\...
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206 views

Path integral measure and symmetry

For a generic field theory the path integral measure is defined as, \begin{equation} \mathcal{D}\Phi = \prod_i d\Phi(x_i), \end{equation} where $\Phi$ is a generic field (i.e. it may be scalar, ...
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2k views

Is the electromagnetic force responsible for contact forces? [duplicate]

It is commonly stated that there are four fundamental forces, or interactions, in nature. It is natural to consider which of those is responsible for the normal force we meet in elementary physics. ...
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400 views

Etymology of “Renormalisation”

Just out of curiosity, does anyone know why "renormalisation" is so named? Who first came up with the term, and why was it used? I did a mathematics undergraduate so to me "normalisation" means ...
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491 views

What determines the spin of fields in gauge field theories?

I understand that gauge bosons transform as the adjoint of their respective symmetry groups, but what determines the spin of the field? Can you have some gauge group where the adjoint is spin zero?
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92 views

What kinds of contributions can be neglected in the leading logarithmic approximation?

I'm looking for some good explanation on leading logarithmic approximation (LLA) in QCD; in particular, what types of contributions can be neglected while assuming LLA?
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Can we obtain non-Lorentzian metric from Lorentzian metric, through renormalization methods?

Since low-energy, non-relativistic thermal field theories are defined in Euclidean spacetime, while high-energy relativistic theories are define in Minkowski spacetime, I was wondering if there are ...
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183 views

Higgs boson sources

Every fundamental interaction in Physics comes from "some bosonic field" or "force carrier", according to QFT. We have 4 fundamental interactions(force carriers): Gravity (Gravitons) ...
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96 views

Exact summation of a sub-class of diagram: do we know the exact solved problem?

In quantum field theories (to be relativistic, (non-)relativistic statistical or whatever), we have the powerful diagrammatic approach at our disposal. Most of the time we can not sum up all the ...
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230 views

Proof of rotational and translational invariance?

If $ϕ^† ϕ$ is invariant under $SU(2) \times U(1)$, a Phys.SE question I recently posted, then does that mean $ϕ^† ϕ$ is invariant under rotations and translations?
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Problems with putting mass on Yang-Mills theory by hand

When Yang-Mills field theory was introduced, a problem is that the gauge invariance can not allow mass for the gauge field. Later people invented spontaneous symmetry breaking and Higgs mechanism to ...
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552 views

Is there a general relationship between the conformal weight of a field and its (classical) scaling dimension?

A field $\phi(z)$ has the conformal weight $h$, if it transforms under $z\rightarrow z_1(z)$ as $$ \phi(z) = \tilde{\phi}(z_1)\left(\frac{dz_1}{dz}\right)^h $$ The (classical) scaling dimension can ...
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181 views

BRST transformation of adjoint spinor

in Yang-Mills-Theory with matter fields a dirac spinor $\psi$ transforms under BRST as $$\psi \to \delta_\Omega\psi=i\eta\psi $$ with $\eta$ being a ghost field. If I want to get the transformation of ...
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1answer
289 views

'Validity' of QED/QCD/Electroweak interaction

I am currently attending a course on Quantum Field Theory and I got into thinking how valid these theories are. As the theory attempts to describe reality only far above the Planck (length) scale, ...
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467 views

Some questions about the free Fermionic partition function on a circle (Ginsparg's CFT lectures)

The following questions are based on these lectures, http://arxiv.org/abs/hep-th/9108028 I would like to know what is the relationship between the last equation on page 82 ($(L_0)_{cyl} = L_0 - \...
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1answer
274 views

vacuum expectation value and Casimir effect

Is it correct to say that the VEV of the SM Higgs is 246 GeV? If so, is the VEV a reflection, or measure, of the Casimir Effect?
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184 views

How do we calculate the Higgs potential? [closed]

What is the Higgs potential and how do we calculate it?
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667 views

The connection between classical and quantum spins

I have two questions, which are connected with each other. The first question. In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
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1answer
2k views

Bound states and scattering length

What is the relationship between bound states and scattering length? What is the relationship between scattering states and scattering length? When we say, potential is 'like' repulsive for positive ...
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Is it really proper to say Ward identity is a consequence of gauge invariance?

Many (if not all) of the materials I've read claim Ward identity is a consequence of gauge invariance of the theory, while actually their derivations only make use of current conservation $\partial_\...
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Discretization of Hamiltonian using finite difference always justified?

I have this continuum version $$ H_{R}=\int dx\psi^{\dagger}(x)(\frac{p^{2}}{2}+V)\psi(x) $$ with $V$ as constant potential. Is it always justified to go from this to $$ \sum_{i}c_{i}^{ \dagger }\...
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What is the relationship between string theory and quantum field theory?

Please forgive a string theory novice asking a basic question. Over at this question Luboš Motl gave an excellent answer, but he made a side comment that I've heard before and really would want to ...
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The phrase “Trace Anomaly” seems to be used in two different ways. What's the relation between the two?

I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing. The first way I've seen it used is in the manner, for ...
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The problem of a relativistic path integral

Many books have described the path integral for non-relativistic quantum. For example, how to get the Schrödinger equation from the path integral. But no one told us the relativistic version. In fact, ...
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1answer
446 views

Non-equilibrium Green functions

How do we use non-equilibrium Green's functions (NEGF) or the Keldysh formalism in the theory of quantum transport? Please take a simple example like the Hopping model with a non-equilibrium ...
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358 views

Kubo formalism application

Suppose I have some pertubative Hamiltonian on the Hubbard Hamiltonian and I want to calculate the change in current in linear response using the Kubo formalism. Now the kind of perturbative ...
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1answer
457 views

What are renormalons from a physics point of view?

This is again a question in the context of this paper about the Exact Renormalization Group. On p 23 and the following few pages, it is explained that for a $\lambda \phi^4$ bare action at the bare ...
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961 views

current operator in Hubbard model

How to derive the particle current operators for the non-interacting and interacting Hubbard model ? Hubbard Hamiltonian is given here with the interaction term: http://en.wikipedia.org/wiki/...
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1answer
257 views

Number operator and Dirac field (with anticommutation relations)

Before using anticommutation relatives the energy, momentum, charge and number operators of the Dirac field have following expressions: $$ \hat {H} = \int \epsilon_{\mathbf p}\left( \hat {a}^{+}_{s}(\...
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387 views

What is the required prerequisite knowledge of QM, for starting QFT?

As a physics bsc student, I have a very limited knowledge of QM: Dirac formalism, Schrodinger equation and simple solutions (oscillators, particle in a given potential, hydrogen-like atom etc). There ...
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354 views

spectral function in condensed matter physics

What is the importance of deriving the results of perturbation theory in condensed matter physics in terms of spectral functions ?
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76 views

How to rearrange the fermions in CohFT?

A simple question about notation of Moore Nekrasov and Shatashvili which makes me confused. Page 3, the authors rearranged the action into a novel form. For D=3+1,5+1,9+1 respectively, the path ...
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2answers
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Particle current operator in general vs Particle current operator for tight binding Hamiltonian

I am referring Mahan Many-Particle Physics. There are 2 particle current operators -one in general and one for the tight binding Hamiltonian. How do we go from the general current operator (1.195 in ...
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399 views

Naturalness arguments and dimensional regularization?

How do issues of naturalness arise when regularizing QFT using dimensional regularization? I can only recall ever seeing naturalness arguments (hierarchy problem, cosmological constant problem, etc.) ...
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114 views

Types of Solitons

In the condensed matter literature, I have seen broadly two types of solitons which are dark and bright corresponding to fall and rise in density. (I know only the number density case ). But among the ...
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1answer
954 views

The divergence in QCD Series— How many are they, and what do they mean?

I am referring to this question, and especially this answer. In addition, QCD has - like all field theories - only an asymptotic perturbation series, which means that the series itself will ...
6
votes
2answers
316 views

AdS/CFT and boundary translational invariance

I work in quantum information theory/condensed matter and have some very basic questions about AdS/CFT correspondence. For simplicity, I would like to restrict to 1+1 CFT <-> 2+1 AdS. I apologize ...
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104 views

Hamiltonian opeator for quantum field theory

I just started to read Srednicki's QFT and I have a problem here. I thought the order of creation operator and projected hamiltonian should be in reversed order ( here I mean H ~ wba, where a is ...
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1answer
261 views

Reason behind canonical quantization in QFT?

Reason behind canonical quantization in QFT? In the scalar field theory we simply promote the scalar field, $\phi(x)$ to a set of operators: $\hat{\phi}(x)$. What is the reason behind this?
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1answer
185 views

Anticommutation relations and bispinor field

In a case of free Dirac field we have $$ \hat {H} = \int \epsilon_{\mathbf p}\left( \hat {a}^{+}_{s}(\mathbf p )\hat {a}_{s}(\mathbf p ) - \hat {b}_{s}(\mathbf p )\hat {b}_{s}^{+}(\mathbf p ) \right)...
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2answers
540 views

Why is a general Green's function invariant under translations?

I am struggling to understand Green's functions, as used in Quantum Field Theory. One of my main problems is that the source I have been reading has a definition which is certainly correct, but ...
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1answer
645 views

How to get the $i\epsilon$ prescription for a Faddeev-Popov ghost propagator?

In path integral formalism, for a physical field there will be an $i\epsilon$ term in the action, which comes from identifying the in and out vacuum, and in turn this $i\epsilon$ will naturally appear ...
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Mass frequency problem

For Dispersion relation , according to Gaussian profile, the author in the equation 3 wrote as $\omega= \left(k^2+\omega_{mass}^2\right)^{1/2}$ My question is what is mass frequency and how it arose ...
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1answer
262 views

What happens to the wave function after applying the D'Alembert operator?

Is the result of applying the D'Alembert operator on a wave function always zero? Or are there exceptions?
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1answer
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quantum mechanics current operators

How to derive the charge current and the energy current operators in second quantized form in Quantum mechanics ? Also if you could comment in a similar way on the entropy current operator, that will ...
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1answer
389 views

Why do we use spinors for describing fermions?

I.e., what properties of the spinors gives us a reason for using them for describing of wavefunctions of fermions?
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458 views

In spontaneous symmetry breaking, global symmetry broken by gauged subgroup?

My question is simple. Given a group $G$ broken to a subgroup $H$, gauging a possibly different subgroup Hg breaks explicitly the global symmetry $G$, generating what is known as pseudo-Goldstone ...
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Noether current for a local gauge transformation for the Klein-Gordon Lagrangian

The Noether current corresponding to the transformation $\phi \to e^{i\alpha} \phi$ for the Klein-Gordon Lagrangian density $$\mathcal{L}~=~|\partial_{\mu}\phi|^2 -m^2 |\phi|^2$$ by finding $\...
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Spontaneous symmetry breaking by axions?

I am just reading at the beginnin of this nice article, that axions could be responsible for spontaneously breaking of a symmetry in the early universe. Does anybody know which symmetry is alluded to ...
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339 views

Anyons without fractional spin?

Is it possible to have particles obeying anyonic statistics but not having fractional spin? I am wondering, because while spin in quantum physics arises from the geometry/topology of spacetime, ...