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 ...

learn more… | top users | synonyms (1)

1
vote
1answer
88 views

Bogolubov coefficient identities

Along the lines of Birrell and Davies, which contrary to Mukhanov-Winitzki (which is actually my level) gives a quite general but short account on Bogolubov transformations, I tried to follow the ...
0
votes
1answer
111 views

Is Hyperbolic Space $H3$ the best representation space for momenta, in momentum-scale invariant theories?

The motivation is the following: For each particle of mass m, we could write : $- (E/m)^2 + (p_x/m)^2 + (p_y/m)^2 + (p_z/m)^2 = -1$, which is nothing than a equation for a point in the ...
1
vote
0answers
335 views

Newton's gravitational constant $G$, the reduced Planck constant $\hbar$, the speed of light $c$: the Dream Team of moderators?

The three great constants of Nature are well known: the speed of light $c$ (special relativity), the reduced Planck constant $\hbar$ (quantum mechanics), Newton's ...
1
vote
1answer
193 views

Definition of CFT

A standard QFT cannot be defined as a set of Poincare-invariant correlation functions because this does not take into account the possibility of non-perturbative effects (e.g. instantons) Can we ...
3
votes
2answers
187 views

Dark matter: degrees of freedom

I'm afraid this question could sound a little too vague. I don't even know if dark matter (DM) can be genuinely described by quantum field theory, or if quantum field theory should be somehow ...
5
votes
1answer
297 views

Particle sources and particle detectors in quantum field theory

I am looking for a resource that clearly exposes the concepts of a particle source and a particle detector in the context of Quantum Field theory. I want to understand Irreversibility in this context. ...
4
votes
3answers
932 views

Creation of particle anti-particle pairs

I was reading some QFT notes and there is one point that I don't understand, they are justifying why we need QFT saying that the number of particles is not preserved once we consider special ...
0
votes
0answers
69 views

Books dealing with Quantum field theory [duplicate]

Possible Duplicate: What is a complete book for quantum field theory? I am looking for good books that deal with Quantum Field theory starting from basics. Please suggest something that ...
8
votes
3answers
556 views

How can perturbativity survive renormalization?

The most usual way to renormalize quantum field theories is by re-writing the Lagrangian in terms of physical (finite) parameters plus counter-terms. Take $\lambda \phi^4$ theory for instance: $$ ...
6
votes
3answers
2k views

Do strong and weak interactions have classical force fields as their limits?

Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
6
votes
2answers
733 views

Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
2
votes
2answers
299 views

Fermion Field of Standard Model

Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
2
votes
2answers
1k views

How to obtain Dirac equation from Schrodinger equation and special relativity?

I'm reading the Wikipedia page for the Dirac equation: The Dirac equation is superficially similar to the Schrödinger equation for a free massive particle: A) ...
0
votes
0answers
117 views

Good introductory books on AdS/CFT correspondence [duplicate]

Possible Duplicate: Introduction to AdS/CFT Since my question in a similar topic was deleted, I'll ask away and hope ppl won't come here telling me: this was already asked! :\ I have a ...
3
votes
1answer
1k views

How to construct the charge conjugation matrix for any given dimension?

Generally, Gamma matrices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally ...
4
votes
3answers
241 views

Odd number of second class constraints (!)

For my thesis, I have calculated the constraints for a system using Dirac method of constraint analysis. The problem is I got odd number of second class constraints (!), which gives me unusual numbers ...
6
votes
1answer
361 views

Quantum Field Theory: why fields are equal to zero on the boundary?

One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is $$ \phi(x)=0\,\text{on the boundary} $$ and this is widely used in many situations ...
1
vote
2answers
321 views

momentum four vector and dirac matrices

$$c\left(\alpha _i\right.{\cdot P + \beta mc) \psi = E \psi } $$ From the above dirac equation it can be shown for zero momenta that spin and antimatter are associated with $\beta $. On the other ...
2
votes
3answers
205 views

Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?

An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
3
votes
1answer
125 views

Is matrix picture of quantum mechnics further used in QFT and superstring theories?

Just curious: is matrix picture of quantum mechnaics further used in QFT and superstring theories? It seems like not....
7
votes
4answers
2k views

Calculating the commutator of Pauli-Lubanski operator and generators of Lorentz group

The Pauli-Lubanski operator is defined as $${W^\alpha } = \frac{1}{2}{\varepsilon ^{\alpha \beta \mu \nu }}{P_\beta}{M_{\mu \nu }},\qquad ({\varepsilon ^{0123}} = + 1,\;{\varepsilon _{0123}} = - ...
3
votes
2answers
288 views

Ordering Ambiguity in Quantum Hamiltonian

While dealing with General Sigma models (See e.g. Ref. 1) $$\tag{10.67} S ~=~ \frac{1}{2}\int \! dt ~g_{ij}(X) \dot{X^i} \dot{X^j}, $$ where the Riemann metric can be expanded as, $$\tag{10.68} ...
8
votes
1answer
3k views

Proof of Yang's theorem

Yang's theorem states that a massive spin-1 particle cannot decay into a pair of identical massless spin-1 particles. The proof starts by going to the rest frame of the decaying particle, and relies ...
3
votes
2answers
432 views

Why is fractional statistics and non-Abelian common for fractional charges?

Why non integer spins obey Fermi statistics? Why is fractional statistics and non-Abelian common for fractional charges?
10
votes
4answers
4k views

Lagrangian to Hamiltonian in Quantum Field Theory

While deriving Hamiltonian from Lagrangian density, we use the formula $$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$ But since we are considering space and time as parameters, why the formula ...
3
votes
2answers
416 views

2D Ghost CFT and two-point functions

For some reason I am suddenly confused over something which should be quit elementary. In two-dimensional CFT's the two-point functions of quasi-primary fields are fixed by global $SL(2,\mathbb ...
3
votes
1answer
516 views

Interpretation of field operator

Consider a real scalar field operator $\varphi$. It can be written in terms of creation and anihilation operators as $$\varphi(\textbf{x})=\int \tilde{dk}[ ...
1
vote
1answer
286 views

Importance of phase in probability amplitude in QFT

I have started teaching myself QFT from the textbook by A. Zee. From reading that book, my idea of a path integral in field theory is the probability amplitude to go from a given field configuration ...
3
votes
1answer
285 views

scattering singularity

In QFT when one works out the cross section between two colliding electrons one gets a formula which is proportional to $\theta^{-4}$ where $\theta$ is the scattering angle which is due to a nearly ...
8
votes
2answers
572 views

What's the deepest reason why QCD bound states have integer charge?

What's the deepest reason why QCD bound states have integer electric charge, i.e. equal to an integer times the electron charge? Given that the quarks have the fractional electric charges they do, ...
2
votes
1answer
386 views

Killing vectors for SO(3) (rotational) symmetry

I am reading a paper$^1$ by Manton and Gibbons on the dynamics of BPS monopoles. In this, they write the Atiyah-Hitchin metric for a two-monopole system. The first part is for the one monopole moduli ...
3
votes
1answer
1k views

Conservation Laws and Symmetries

Usually, in Quantum Mechanics, an observable is an operator on the space of the possible quantum states (labelled as $|\psi\rangle$). If this quantity is conserved, in the meaning that the associated ...
6
votes
1answer
846 views

simple explanation of chiral anomaly?

Can somebody provide a fairly brief explanation of what the chiral anomaly is? I have been unable to find a concise reference for this. I know QFT at the P&S level so don't be afraid to use math.
6
votes
1answer
1k views

What is the essence of BCFW recursion techniques?

I have recently briefly read about new methods as the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion method. Can anybody please tell me about the essence of it? What does it mean for the ...
9
votes
1answer
199 views

Why are topological solitons present in some phases for lattice models?

Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
7
votes
0answers
148 views

gravitational convergence of light

light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it ...
0
votes
0answers
410 views

Longitudinal and transverse part of vector field components

I was reviewing a paper of coupling to vector field and tensor field. I have got stuck with the term $$A_k \varepsilon^{kmn}\partial_mV_n=V^{T}.(\nabla\times A^{T})-\nabla.(A^{T}\times ...
0
votes
1answer
698 views

Find Trace of Dirac Matrix

The matrices present in the Dirac equation must have the following properties: $\{a^j,a^k\}_{ab} = 2\delta^{jk}\delta_{ab}$ $\{a^j,\beta\} = 0$ $(\beta^2)_{ab} = \delta_{ab}$ How can one show ...
3
votes
1answer
909 views

Why doesn't the Klein-Gordon equation allow for conservation of probability?

I read somewhere that the Klein-Gordon equation doesn't allow for conservation of probability. Can someone prove this mathematically?
2
votes
1answer
369 views

Equivalence of classical and quantized equation of motion for a free field

Suppose a classical free field $\phi$ has a dynamic given in Poisson bracket form by $\partial_o\phi=\{H, \phi\}$. If we promote this field to an operator field, the dynamic after canonical ...
0
votes
1answer
219 views

What is changed when proton has finite radius?

How the field and interactions are changed when we assume that proton has finite radius in atom for example? What gives the finite size effect? Is it the higher moments of multipole expansion?
4
votes
1answer
332 views

What is a virtual photon pair?

When describing a black hole evaporation in the hawking black body radiation it is usually said that is due to a virtual photon pair, is it this what happens? And what is virtual photon pair, does the ...
8
votes
3answers
469 views

Is the commutation of all possible operators sufficient to identify a spacelike interval?

It has been claimed (e.g. here) and apparently already been established, that the interval $x - y$ being (called) "spacelike" implies that $\bigl[\hat O (x),\, \hat O' (y)\bigr]=0$ for any two (not ...
3
votes
0answers
260 views

Pseudo scalar mass and Pure scalar mass

Since the only difference between pseudo scalar and a scalar term is just a change of sign under a parity inversion, is it possible that both of them be present in the same field and interact? For ...
0
votes
1answer
905 views

What is the relationship between the Higgs field and quarks?

I have some difficulty considering the relative size of each and the meaning behind the shape of Higgs boson. I ask relating to the structures of both the Higgs field and quarks. How is it that the ...
3
votes
3answers
911 views

What is the difference between manifest Lorentz invariance and canonical Lorentz invariance?

I often read that the Lorentz symmetry is manifest in the path integral formulation but is not in the canonical quantization - what does this really mean?
5
votes
1answer
371 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 ...
10
votes
1answer
419 views

Does string theory provide a physical regulator for Standard Model divergencies?

In other question, Ron Maimon says that he thinks string theory is the physical regulator. I did not know that string theory regularize divergencies. So, Q1: How does string theory regularize the ...
5
votes
1answer
323 views

Relativistic contraction for a wave packet and uncertainty on momentum

Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
12
votes
3answers
3k views

Gentle introduction to twistors

When reading about the twistor uprising or trying to follow a corresponding Nima talk, it always annoys me that I have no clue about how twistor space, the twistor formalism, or twistor theory works. ...