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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 this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.

6 votes

Interacting representation of the Poincaré group

There is no rigorous proof for this, as there is no known way to make sense of the interaction part of a local Hamiltonian at fixed time in such a way that $H$ becomes self-adjoint. The reason is that …
Arnold Neumaier's user avatar
1 vote
Accepted

Current formula and form factor

Your term is allowed, and in fact present in QED. It gives the anomalous magnetic form factor contribution to the current. In QED, The number $2F(0)$ is the anomalous magnetic moment of the electron. …
Arnold Neumaier's user avatar
1 vote

Questions concerning some parts of the section on one-particle states in Weinberg's first vo...

''Choosing'' the momentum states orthonormal works because momentum states are joint eigenstates of the (commuting, Hermitian) components of momentum, not because one can make arbitrary choices. For …
Arnold Neumaier's user avatar
2 votes

Where can one learn about dispersion relations for S-matrices?

Bjorken & Drell's QFT book. It is old but therefore strong on this point.
Arnold Neumaier's user avatar
1 vote

Quantum State of Photon Question

Photons always have spin 1, this means that they have two transversal polarization indices - not spin indices, just as in the classical case. In the helicity formalism, the two indices describe left …
Arnold Neumaier's user avatar
1 vote

In, QFT, do the excitations in the quantum fields exist physically?

Properties of the quantum fields (its mass density, charge density, response to external fields, etc.) can be measured and predicted in the same way as all quantum observables. There is therefore noth …
Arnold Neumaier's user avatar
4 votes
Accepted

Coherent state of charged field

There is an extensive survey paper by Zhang, Feng, and Gilmore that discusses coherent states for many different systems, both from a theoretical and a practical point of view. In particular, their un …
Arnold Neumaier's user avatar
1 vote

What is the exact definition of 'consistent field theory'?

The paper referenced, http://www.sciencedirect.com/science/article/pii/0550321375902795 states the assumptions on the genrator of a symmetry or supersymmetry in Section 2: (i) it commutes with the S- …
Arnold Neumaier's user avatar
8 votes

The energy spectrum in quantum field theory

As the four components of the momentum vector commute, the right spectrum to consider is the joint spectrum of the momentum; the energy spectrum alone is far too degenerate. Because of Lorentz symmetr …
Arnold Neumaier's user avatar
1 vote

Energy spectrum, mass spectrum, and mass gap

The lack of a mass gap goes in all interesting cases together with the existence of a massless particle. These don't have a rest frame. See, e.g., the section ''What is the mass gap?'' in my theoretic …
Arnold Neumaier's user avatar
11 votes
1 answer
773 views

Landau poles in dimension <4?

It is well-known that QED and $\Phi_4^4$ quantum field theory have (in renormalized perturbation theory) a Landau pole and therefore are not asymptotically free. Is this specific to 4-dimensional QFT, …
Arnold Neumaier's user avatar
3 votes

Interpretation of an "interaction" term

In principle, yes, but only if the expectation value of $\phi$ is nonzero, so $\phi$ would immediately be shifted. Moreover, the result would be badly nonrenormalizable, so nobody is using such terms. …
Arnold Neumaier's user avatar
2 votes
Accepted

Anomalous magnetic moment of electron

g=2 comes from the Dirac equation, and is a relativistic effect. In the Pauli equation, it would have to be added by hand. Radiation corrections give additional terms to the Dirac equation and modif …
Arnold Neumaier's user avatar
3 votes

Quantum harmonic oscillator

I think the analogy with the bowls is not really appropriate. If one thinks of things oscillating at each point in space, these oscillations are heavily correlated, due to the field equations. Indep …
Arnold Neumaier's user avatar
1 vote

Conceptual quantum field theory

E. Zeidler, Quantum Field theory I Basics in Mathematics and Physics, Springer 2006. http://www.mis.mpg.de/zeidler/qft.html is a book I highly recommend. It is the first volume of a sequence, of whic …
Arnold Neumaier's user avatar

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