All Questions
Tagged with resource-recommendations mathematical-physics
122 questions
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Reference on the quantization of Polyakov action at higher genus
Despite my searches, I was unable to find a good reference on this topic. I was looking for a reference about quantization of the Polyakov action for an arbitrary Riemann surface. I am thankful to ...
1
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1
answer
134
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Where can one learn about the cluster expansion without a background in statistical mechanics?
Apologies if this is better suited for mathSE. I would like to learn about the cluster expansion as is used in rigorous quantum field theory. I have read a lot on QFT, both from a physics and ...
2
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0
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79
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Quantum Mechanics book with good treatment on unbounded operators [duplicate]
I'm looking for a certain kind of approach to quantum mechanics. In most places I've looked, almost all of the exposition on how to employ construct observables in quantum mechanics is that of compact ...
4
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0
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64
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References discussing renormalizability via Sobolev norms
Hawking & Hertog's paper Living With Ghosts has a nice introduction in which the authors discuss the issue of renormalizability of a field theory in terms of Sobolev norms. More specifically, they ...
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58
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Mathematical references for gauge theory in condensed matter physics
I am currently trying to go through some literature on the classification of symmetry protected topological phases. Primarily, I am interested in the classical of topological phases using mathematical ...
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77
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Use of mathematical structure on physics [closed]
I want resources for studying in detail the connection between the mathematical structures of physical theories and said physical theories.
For example, i know what a Hilbert space or a principal ...
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74
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$\mathbb Z_N$ (discrete) gauge theory
I am currently trying to go through some literature on symmetry protected topological phases and gauge theories defined on lattices. I am looking for a mathematically precise reference that discusses $...
4
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90
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References for Exterior Differential Systems for physicists
Many problems in classical mechanics, classical and quantum field theory among others require the study of systems of partial differential equations where questions like existence and uniqueness ...
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573
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Nuclear spectral theorem in Rigged Hilbert Spaces (Gelfand-Maurin theorem)
Before I go into the question, I would like to mention that I am a physicist with some formal mathematical knowledge, but not expert in functional analysis.
In physics, we very often say: Let $|x \...
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1
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111
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Newtonian Mechanics in first-order logic
I asked a similar question before, but it did not give the answer I was looking for, so I will clarify what I actually want in this question. H. Andreka created a formal first-order logic theory that ...
3
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1
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971
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Pre-requisites for V.I. Arnold's mathematical methods for classical mechanics
I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, ...
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201
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HaMiDeW coefficients - recursive calculation of the coincidence limits
In his book Aspects of Quantum Field Theory in Curved Spacetime Stephen Fulling calculates the coincidence limit $[a_1]$ and gives an idea of how $[a_n]$ with $2 ≤ n$ can be found recursively.
Since ...
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References on the relation between path integrals and algebraic QFT
I am wondering on whether there are any references discussing how path integrals relate to the algebraic approach for quantum field theory. More specifically, in the algebraic approach, states are ...
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135
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Mathematically Rigorous Introduction to the Standard Model [duplicate]
I am looking for textbooks, lecture notes, lecture videos on a rigorous introduction to the standard model of elementary particles. I'd prefer to not be referred to monographs for an introduction as ...
2
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0
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472
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Mathematically Rigorous Introductory Resources for Condensed Matter Physics
I am looking for textbooks, lecture notes, lecture videos on rigorous introductions to condensed matter physics. I'd prefer to not be referred to monographs for an introduction as they tend to be ...
3
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1
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71
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Resources on Post-Einsteinian Results in GR
What are some good books, lecture notes, articles, etc. that can be used as introduction to the landscape of major results in general relativity since Einstein? In terms of the timeline, I'm thinking ...
2
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1
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319
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Recommendations for Algebraic quantum mechanics book
I am familiar with quantum mechanics and quantum information at the level of Sakurai and Preskill's lecture notes / Nielsen and Chuang. I want to study the $C^*$ algebraic formulation of quantum ...
18
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1
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Mathematically rigorous QFT text
There are multiple questions on here about QFT textbook recommendations, but I am looking for mathematically precise texts on QFT.
Recommendations of introductory and advanced texts are welcome, but ...
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218
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Reference Request: Mathematical Foundations of Physics
I am looking for reading on examples, or preferably a comprehensive summary on how the foundations of mathematics are related to physical theory. I would like to know whether basic set-theoretic and ...
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2
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334
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Quiver Mechanics
What do you suggest as an essential and introductory set of references in Physics literature for learning quivers? Any textbook?
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1
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105
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Literature recommendations for the relationship between fundamental physics and pure mathematics?
So, I have been reading up on the works by Kenneth Wilson, mainly his 3 statements that he concluded to be true about our universe. His first: 'There exists a hierarchy to our universe'. From this i ...
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55
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Topological Field Theory for Physicists [duplicate]
I was wondering if anyone knows good resources for Topological Field Theories aimed at physicists. In particular, I am looking for references which are full of examples, starting with simple toy ...
5
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1
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515
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References on mathematical stacks for a string theory student
This question was posted on mathoverflow (here) without too much success.
I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" ...
3
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1
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817
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Prerequisites for IAS volumes on Quantum Fields and Strings
I'm a physics grad student interested in pursuing physics in a mathematically rigorous manner. However, I've hit a roadblock with the two volume book, Quantum Fields and Strings: A Course For ...
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1
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91
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Instantons in mathematical physics [closed]
I am extremely curious about instantons in the context of mathematical physics, and I would like to learn more about the subject. Could anyone give me good references about this? Especially references ...
2
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0
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73
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References for topological strings on supermanifolds
This question concerns topological string theory.
It was known sice its outset, that the BRST-cohomology ("the ring of observables") of the weakly coupled B-model topological string on a ...
2
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1
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94
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What is best book on self-adjoint extensions?
I need to understand self-adjoint extensions in quantum mechanics to solve some problems of scattering and bound states in Aharonov-Bohm potentials. There are some referencies that present the math ...
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1
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94
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Solution set: Mathetmatical Methods For Physics [closed]
Recently, I had a good start with H.W. Wyld on mathematical methods for Physics and now looking forward to ask whether is there any solutions available for the problems given at the end of each ...
7
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92
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Lost reference: Kähler gravity in six dimensions and three dimensional $SL(2,\mathbb{C})$ Chern-Simons theory
I've noticed that several references take for a fact that by studying Kähler gravity on a Calabi-Yau threefold one can demostrate that any lagrangian submanifold embedded in the threefold posees three ...
7
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1
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692
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What are some good references for field theory via functional analysis?
Many of the aspects of QFT are traditionally done in ways incompatible with a rigorous mathematical treatment, calling for a variety of tricks to fix essentially what was caused by unjustified ...
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0
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23
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Source for Learning? [duplicate]
I am an very ameteur mathematician and physicst (If I can say mathematician and physicst to myself xD). I want to learn topics in physics. Like electromagnetism, mechanic, thermodinamics etc. But I ...
8
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2
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1k
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Discussion: Mathematically precise physical textbooks [closed]
I am very interested in the abstract mathematical description of nature. Therefore, I have recently started to compile a list of good textbooks about physics, which have a very high level of ...
4
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1
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469
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Is there any book that treat time-dependent perturbation theory with rigorous mathematics?
I am searching for rigorous mathematics books or notes for time dependent perturbation theory.
For introductory quantum mechanics there is the excellent book spectral theory and quantum mechanics ...
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Advice needed on learning maths oneself [duplicate]
I am a master's student in physics trying to learn maths on my own. My classes workload is heavy and the schedule is very hectic due to which I don't get time to do mathematics.
I have done Linear ...
8
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2
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2k
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Book recommendations for Fourier Series, Dirac Delta Function and Differential Equations?
I'm a second-year undergrad and currently taking a course in Mathematical Physics which covers the topics of Dirac delta functions, Fourier series, Fourier transforms and Differential equations. They ...
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1
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1k
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Which are the best mathematical methods books for which topic for a physics undergrad? [duplicate]
I am a physics undergraduate and I would be glad if you share your opinion about which books are best for which topics in mathematical methods, from very basic to advanced. (Like you some say Tom ...
3
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1
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211
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References of Deficiency indices theorem (von Neumann)
I am looking for proof or some interpretation around why the domain of the new extension $D(A_U)$ in the Theorem below is given by its specific formula.
I have already searched in papers and here but ...
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63
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Recommended books for introduction to Quantum Mechanics for students who are mathematically aligned [duplicate]
I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on ...
1
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0
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414
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Book recommendation on Quantum Mechanics which is a bit mathematically aligned and gives good introduction to Hilbert Space for beginners [duplicate]
I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on ...
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1
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154
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Can there be an **essential topic** in physics which cannot be archimedean? [closed]
In physics it seems everything is explained with $\mathbb R$ or $\mathbb C$ typed entitites.
Is there anything in or that would be in future in physics that would need the utility of $p$-adics in an ...
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Relationship between boundary states and primary states of a Kazama-Suzuki model
In [1] and [2] the authors claim that the boundary states (not just the Ishibashi states) of a Kazama-Suzuki model are labelled in the same way as the primary states of the model, so that the boundary ...
1
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0
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33
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Book on tetrads formalism and tetradic formulation of General Relativity [duplicate]
Could anyone give me some references for mathematicians (coordinates free notation, formalism of fiber bundles etc.) about tetrads, Palatini-Cartan theory, stuff about formulation of GR with tetrads?
...
4
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0
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172
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Looking for lecture videos that follow Arnold's Mathematical Methods of Classical Mechanics [duplicate]
I'm an undergrad and I'm looking for lecture videos (on youtube and such) that follow this textbook.
My course roughly follows it, but glosses over some mathematical details that I feel would be ...
0
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0
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147
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Complex Analysis Textbook using Fluid Dynamics
This is a literature request. I remember being told of a Complex Analysis textbook that teaches the Cauchy-Riemann equations and Potential Theory using Fluid Dynamics. Does anyone know who the ...
5
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1
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217
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Reference Request: Basis-independent formulation of tensor networks
I could not find any references for a basis-independent formulation of tensor networks: All papers I have found use pretty much (explicitly or implicitly) the canonical computational basis by defining ...
1
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1
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253
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Spectral theorem for unbounded self-adjoint (hermitian) operators
It is my understanding that in quantum mechanics we use self-adjoint operators (that is an axiom of the theory). This operators can be either bounded or unbounded, being the latter the more general ...
7
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690
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Rigorous treatment of Penrose diagrams
I'm looking for a rigorous exposition of Penrose diagrams (also called conformal diagrams in general relativity. By "rigorous" ("careful" is perhaps a more attractive word) I mean that it should ...
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3
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210
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References for examples of $\ast$-algebra approach to QM and QFT
In studying QFT on curved spacetime I've found the $\ast$-algebra approach as one viable approach to the subject on the paper Quantum Fields in Curved Spacetime by Wald.
The $\ast$-algebra approach ...
4
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Book with problem sets that will go well with Dennery and Krzywicki's Mathematics for Physicists? [duplicate]
Does anyone have any book/problem sets that would go well with Dennery and Krzywicki's Mathematics for Physicists? I like the style of the book compared to usual texts like Riley, Arkfen, or Hobson ...
14
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1
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1k
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Representations of the Lorentz group in an arbitrary number of space-time dimensions$.$
Let $\mathrm{SO}(1,d-1)^\uparrow$ be the connected Lorentz group in $d$ dimensions. I am looking for a book/article where its finite-dimensional projective representations are studied in detail. ...