Questions tagged [quantum-field-theory]

Use this tag for questions about quantum field theory in theoretical/mathematical physics. Quantum Field Theory is the theoretical framework describing the quantization of classical fields allowing a Lorentz-invariant formulation of quantum mechanics. Associate with [tag:mathematical-physics] if necessary.

Quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics and is used to construct physical models of subatomic particles in particle physics/high-energy physics, quasiparticles in condensed matter physics and highly relevant to statistical field theory.

QFT treats particles as excited states (also called quanta) of their underlying fields, which are — in a sense—more fundamental than the basic particles. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding fields. Each interaction can be visually represented by Feynman diagrams, which are formal computational tools, in the process of relativistic perturbation theory.

363 questions
10
votes
1 answer

Category Theory and Quantum Mechanics

I am wondering if particle interactions in quantum theory can be modeled as a morphism between $2$ categories. My reasoning is that since the states of particles are modeled as vectors in a Hilbert space, given two Hilbert spaces, call them $A$ and…
10
votes
2 answers

What is a particle mathematically?

In quantum field theory, what is a particle mathematically? How would you explain to someone who kows alot of math but no physics what a particle is? A simple example model would suffice.
Enough
  • 127
  • 4
10
votes
1 answer

What is quantum field in terms of mathematics?

I am reading a book on quantum field theory, while I have never been trained as a physicist. I found a big gap in language and have trouble understanding what physicists mean by "quantum field". If I understand correctly, after quantizing twice…
9
votes
1 answer

Why is Grassman integration so weird?

Why are Grassman integration and differentiation equivalent? The only justification of this definition I have ever scene is "Well, how else could it work?" Indeed, I don't have any other suggestions, but I'd like something a bit more rigorous or…
ZachMcDargh
  • 250
  • 1
  • 8
9
votes
1 answer

Mathematical background for TQFT

I am physicist. I`ve started studying Topological QFT. What would you recommend to read in mathematical field for understanding Witten’s old articles of 80s-90s? What books/articles could help form proper mathematical background for TQFT?
9
votes
0 answers

Motivation for quantum cohomology rings

I can't seem to find a good source for the motivation for defining the big quantum cohomology ring with its quantum product. Collecting the Gromov-Witten invariants in a generating function seems like a sensible thing to do (and is supposedly…
9
votes
1 answer

In what sense is quantum field theory mathematically incomplete?

Is the Yang-Mills existence and mass gap (Millenium Prize problem) essentially what is required? Or are there more problems in putting QFT on strong mathematical foundations? For example, the exsitence of measure in doing functional integration in…
user68441
  • 91
  • 1
9
votes
2 answers

Mathematical significance of the "Dirac conjugate"

Let $\psi$ be a Dirac spinor. The so-called "Dirac conjugate" of $\psi$ is defined to be $\widetilde{\psi}:=\psi ^*\gamma ^0$, where $^*$ denotes the adjoint and the gamma matrices $\gamma ^\mu$ comprise the essentially unique irreducible…
9
votes
4 answers

Gentle introduction to fibre bundles and gauge connections

To better understand papers like this for example, which makes heavy use of fibre bundles and gauge connections to represent gauge fields, I am looking for a nice introduction to this topic. The only thing I have read so far is the corresponding…
9
votes
0 answers

What are the mathematical foundations of the renormalisation group?

Briefly, RG refers to mathematical tools that allows systematic investigation of the changes of a physical system as viewed at different distance scales. These methods are very important in quantum field theory and statistical mechanics. I'm…
8
votes
1 answer

Evaluation and Coevaluation maps of a TQFT

In Lurie's On the Classification of Topological Field Theories, he states in Proposition 1.1.8 that for an oriented compact manifold $M$ and a TQFT $Z:\mathrm{Cob}(n)\to \mathrm{Vect}_k$, there is a perfect pairing $Z(\overline{M})\otimes Z(M)\to…
8
votes
1 answer

Show $\lim\limits_{t\to\infty}\Bigg|\sum\limits_{n=0}^\infty\Theta(t-nR)\frac{(\Gamma(t-nR))^n}{n!}e^{-\Gamma(t-nR)}\Bigg|^2=\frac1{(1+\Gamma R)^2}$

I have encountered the following problem while studying non-Markovian effects in real-time dynamics of open quantum systems. In particular, I was studying a system comprised of two qubits (qubit is a standard shorthand for two level quantum system)…
7
votes
0 answers

Cauchy representation and branch point order

This question is about the nature of branch points which arise in certain Cauchy-integral representations of functions of a single complex argument, $z$. The main application is for dispersion relations but we can ignore that connection since this…
7
votes
0 answers

Reference for Dimensional Regularization

I am studying a bit of theoretical physics (QFT and string theory), and I obviously stumbled upon dimensional regularization. I have been told that this technique has in fact a solid mathematical theory behind. I'd like to learn more on this, and I…
7
votes
1 answer

Formal Definition of Yang Mills Lagrangian

I have a question regarding the Lagrangian in non abelian gauge theory. Say, $G$ is the gauge group and $\mathfrak g$ the associated Lie algebra. The Lagrangian is often written as $$ \mathcal L=-\frac {1}{4} \text{tr} (F_{\mu \nu} F^{\mu \nu}) +…
1 2
3
24 25