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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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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3k views

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 ...
8
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2answers
2k views

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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2answers
1k views

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
437 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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356 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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448 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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2answers
954 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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2answers
370 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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3answers
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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0answers
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
1k views

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 ...
6
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388 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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112 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 ...
16
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1answer
942 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
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2answers
314 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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0answers
103 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
258 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
528 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 ...
6
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1answer
638 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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0answers
72 views

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
1k views

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 ...
3
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1answer
378 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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2answers
452 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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2answers
1k views

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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0answers
154 views

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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1answer
336 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, ...
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2answers
1k views

Equivalence Theorem of the S-Matrix

as far as I know the equivalence theorem states, that the S-matrix is invariant under reparametrization of the field, so to say if I have an action $S(\phi)$ the canonical change of variable $\phi \to ...
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1answer
220 views

Is the Schwinger action principle important in renormalization?

Is the Schwinger action principle important in renormalization? I want to know if this principle could help us to see if a model is renormalizable of not. If you have any other comment or information ...
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0answers
88 views

Dimension dependence

The question is related to this one The time averaged total energy, $\bar E$, has the following $\varepsilon$ expansion in $D$ dimension: \begin{equation} \bar{E}=\varepsilon^{2-D}\frac{E_0}{2\lambda}...
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3answers
616 views

Dimensions in lagrangian potential

According to Mankowski flat space dimensions We can write, $$L= \int \text{dt} \text d^d{x} \left[ \frac{1}{2} \dot\phi^2 - \frac{1}{2} \left(\frac{\partial \phi}{\partial r} \right)^2 -V(\phi)\...
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1answer
443 views

Invariance of Functional Integration Measure

Let us consider the functional integral: \begin{equation} \int \mathcal{D} A e^{iS[A]} \end{equation} where $S[A]$ is the action for $U(1)$ gauge field and \begin{equation} \mathcal{D}A\equiv \...
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4answers
410 views

SUSY and the Large hadron collider

Did the LHC rule out SUSY as a solution to the hierarchy problem ? What's the common belief among theorists regarding the possibility of discovering SUSY in the 2015 run of the LHC ? Did the absence ...
0
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1answer
78 views

Life time of a wave

Let us consider, we have guessed a potential for a wave like non linear, which is propagating through space. We guess a Lagrangian for the wave $$L= \int r^{d-1} dr \left[\frac{1}{2}\dot \phi^2 -\...
4
votes
2answers
610 views

Unitary spacetime translation operator

Srednicki writes: We can make this a little fancier by defining the unitary spacetime translation operator $$ T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar) $$ Then we have $$ T(a)^{-1} \phi(x) T(a) = \...
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1answer
132 views

Formulation of the uncertainty principle for a system?

There is a biological system that I can indeed describe by a simple quantum Hamiltonian $H$ having eigenstates $|q\rangle$ labelled by the numbers $q$, and having energies proportional to $f(q)$ - ...
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0answers
157 views

What is the physical meaning of equivalence of 1st and 2nd quantization formalism?

Ref (Superstring theory (Green, Schwarz, Witten)) Take an $n$ dimensional euclidean space-time $x_0,x_1...x_{n -1}$, a relativist real scalar field, with a propagator $G_E(x,y)$. The propagator ...
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0answers
127 views

Can a hierarchy of fixed points potentially be used to describe a kinetic energy spectrum which is composed of multiple scale invariant subranges?

Making use of a nonequilibrium functional renormalization group (Berges and Mesterhazy, 2012) are able to investigate a whole hierarchy of fixed points that explain the successive evolution of a ...
10
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1answer
604 views

Renormalization is a Tool for Removing Infinities or a Tool for Obtaining Physical Results?

Quoting Wikipedia: renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities. Is that true? to me, it seems better to define ...
1
vote
1answer
165 views

Finding out Energy value

A Lagrangian is given by, $$L= \left(\frac{\pi}{2}\right)^2 R^d \left[\frac{1}{2}\dot A^2 - V(A_{max})\right]$$ $$E=\left(\frac{\pi}{2}\right)^2R^d V(A_{max}) $$ where V (A) now includes nonlinear ...
7
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2answers
637 views

Quantum to classical mapping: quantum criticality and path integral Monte Carlo

I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the ...
17
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3answers
1k views

Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field theory

I wondered if someone could help me understand spontaneous symmetry breaking (SSB) in classical mechanics, quantum mechanics and quantum field theory. Consider a Higgs-like potential, with a local ...
3
votes
1answer
313 views

How can “quantum particles have positive masses, even though the classical waves travel at the speed of light”?

Clay Mathematics Institute writes about the Yang-Mills and mass gap problem on this page http://www.claymath.org/millennium/Yang-Mills_Theory/: The successful use of Yang-Mills theory to describe ...
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0answers
149 views

The interaction picture doesn't exist? [duplicate]

I have recently encountered Haag's theorem and according to Wikipedia: Rudolf Haag postulated [1] that the interaction picture does not exist in an interacting, relativistic quantum field theory (...
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1answer
195 views

How to justify matter-field interaction for non-gauge-invariant Hamiltonian?

I'm wondering how can one formally justify the electromagnetic response of a system which does not verify local U(1) gauge invariance. A good example of what I would like to consider is given by the ...
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1answer
277 views

The unitary time-evolution in the interation picture

I'm currently consuming a course on QFT where we need to define the unitary time-evolution to get the time evolution of the wave function in the interaction picture: $\hat{U}(t_1,t_0) = \exp\left(\...
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1answer
448 views

What is on the AdS side in AdS/CFT supergravity or string theory?

What really is on the AdS side in AdS/CFT, does it always have to be string theory or is sometimes supergravity "enough" or better suited to do calculations? From the answers to my earlier question, ...