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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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 ...
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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: $$ ...
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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?
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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 ...
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Fermion Field of Standard Model

Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
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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) ...
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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 ...
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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 ...
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379 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 ...
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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 ...
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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 ...
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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....
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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}} = - ...
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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} ...
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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 ...
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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?
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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 ...
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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 ...
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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}[ ...
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288 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 ...
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302 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 ...
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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, ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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715 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 ...
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989 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?
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378 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 ...
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228 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?
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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 ...
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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 ...
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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 ...
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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 ...
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978 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?
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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 ...
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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 ...
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329 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 ...
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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. ...
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What's the differences between pseudospin and spin?

It seems that they both transform as an U(2) group, but I've been told that the three components of real spin change signs under inversion while it is not the case for pseudospin. Could someone name ...
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About calculation of anomalous dimension in Peskin and Schroeder's book.

This question is in reference to question 13.2 in the QFT book by Peskin and Schroeder. To put it in general - I would like to know how does one define "anomalous dimensions" if one is given the ...
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Intuition for gauge parallel transport (Wilson loops)

I'm looking for a geometrical interpretation of the statement that "Wilson loop is a gauge parallel transport". I have seen QFT notes describe U(x,y) as "transporting the gauge transformation", and ...
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Showing that electron and positrons have the same absolute charge

In Zee's quantum field theory in a nutshell, 2nd edition, pg 551 he has the charge of a Dirac field written as $Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s ...
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Self energy, 1PI, and tadpoles

I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be ...
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Charge and the Dirac field

In Zee's quantum field theory in a nutshell, 2nd edition, pg 550 he has $Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s \{b^\dagger(p,s)b(p,s)-d^\dagger(p,s)d(p,s)\}$ showing clearly that $b$ ...
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Validity of Cutkosky cutting rules for fermions

It is rather obvious for me that the generalized optical theorem (see e.g. Peskin&Schroeder) must hold for S-matrix elements for fermions as it is directly related to the unitarity of the ...
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Relating theta_QCD to neutron EDM

How do I relate the topological $\theta_\text{QCD}$ parameter to the electric dipole moment (EDM) of the neutron? I am very familiar with chiral perturbation theory. I just need to know how to take ...