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.

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String Theory: What to do?

This is going to be a relatively broad/open-ended question, so I apologize before hand if it is the wrong place to ask this. Anyways, I'm currently a 3rd year undergraduate starting to more seriously research possible grad schools. I find myself in…
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How are topological invariants obtained from TQFTs used in practice?

Topological quantum field theories (TQFTs) are studied for different reasons, as exemplified in the following places: Atiyah, Topological quantum field theory Lurie, Topological Quantum Field Theory and the Cobordism Hypothesis Math Overflow,…
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reference for multidimensional gaussian integral

I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are derived: $$ \begin{eqnarray} & {} \quad \int…
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Mathematical and Theoretical Physics Books

Which are the good introductory books on modern mathematical physics? Which are the good advanced books? I read Whittaker's Analytical Dynamics, and I am reading Arnold's Mathematical Methods of Classical Mechanics. However, I am not very interested…
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Atiyah's definitions of Topological Quantum Field Theory

According to Atiyah, a TQFT is a functor from the category of cobordisms to the category of vector spaces. How does this definition relate with the physics of quantum mechanics? What does the category of cobordism in the above definition represent…
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Functional differential equation (from Quantum Field Theory).

I have a certain differential equation that includes functional derivatives. I know the solution, but I'm having a hard time to show that the equation is indeed solved by the solution. The background for this question is quantum field theory (in…
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Areas of contemporary Mathematical Physics

I have often heard that some developments in Physics such as Gauge Theory, String Theory, Twistor Theory, Loop Quantum Gravity etc. have had a significant impact on pure mathematics especially geometry and conversely. I am interested in knowing a…
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Was von Neumann's 1954 ICM address "Unsolved Problems in Mathematics" outdated?

I recently tried to "explain" the generalized probability theory aspect of quantum theory (as one common part of both quantum field theory and quantum mechanics), in the sense of motivations for the different parts of Qiaochu Yuan's post on…
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Relation between $SU(4)$ and $SO(6)$

This is more of a particle physics question than maths. Since $\operatorname{SO}(6)$ and $\operatorname{SU}(4)$ are isomorphic, how are the fields (say for example scalar fields of ${\mathcal{N}}=4$ Super Yang Mills in $4d$) transforming under 6…
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What is the relation between representations of Lie Groups and Lie Algebras?

If $G$ is a Lie Group, a representation of $G$ is a pair $(\rho,V)$ where $V$ is a vector space and $\rho : G\to GL(V)$ is a group homomorphism. Similarly, if $\mathfrak{g}$ is a Lie Algebra, a representation of $\mathfrak{g}$ is a Lie Algebra…
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Guidance regarding research in Mathematical Physics

I am currently a Master's student in Mathematics. The main focus of my undergraduate programme was on Mathematics. However as a part of the course, I have done some Theoretical Physics courses. In mathematics, my area of interest is…
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Electrodynamics in general spacetime

Let $M\cong\mathbb{R}^4_1$ be the usual Minkowski spacetime. Then we can formulate electrodynamics in a Lorentz invariant way by giving the EM-field $2$-form $\mathcal{F}\in\Omega^2(M)$ and reformuling the homogeneous Maxwell equations…
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What are D-branes (in a topological field theory)?

In the past couple years, I've read many words pertaining to D-branes without feeling I have really comprehended them. In broad terms, I think I get what they're about: They're supposed to serve as habitats for the ends of open strings and can be…
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Quantum mechanical books for mathematicians

I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential geometry. I would like to study the Semiclassic…
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Laymans explanation of the relation between QFT and knot theory

Could someone give an laymans explanation of the relation between QFT and knot theory? What are the central ideas in Wittens work on the Jones polynomial?
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