2
votes
0answers
93 views

Learning Roadmap to Mathematical Physics

Currently, I am a graduate student specializing in algebraic geometry. On the other hand, I have also become extremely interested in the mathematical physics. However, I am not sure what steps I ...
5
votes
1answer
97 views

Guide to mathematical physics?

I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ...
2
votes
1answer
51 views

Electromagnetism and thermodynamics(Statistical mechanics) books for the mathematician?

I found some very good classical and quantum mechanics,special relativity,gauge theory books for the mathematicians,but I couldn't find anything on electromagnetism or thermodynamics,are they of not ...
2
votes
2answers
102 views

Set theory and physics [closed]

I would like to know if there are some physical concepts (preferably accessible ones like force, torque, ...) that can be significantly better understood when looked at in the light of concepts taken ...
1
vote
1answer
24 views

Books for Tensor Algebra used in Physics?

I'm taking a dual Math,Physics undergraduate course.I want to study GR and a few parts of relativistic Quantum Mechanics.I've a decent amount of knowledge in linear algebra. Though we have tensor ...
0
votes
0answers
14 views

Heinrich Hertz on Mathematical Equations

What is the quote from Heinrich Hertz on how he could never exhaust the meaning behind a mathematical equation? (It's not mentioned in the Hertz quotations here.)
5
votes
0answers
121 views

Learning roadmap to Topological Quantum Field Theories from a mathematics perspective

I want to learn TQFT's and am looking for review articles or books. My mathematics knowledge is limited to one year of graduate course in Algebra (Groups,Rings,Fields,Categories, Modules and ...
1
vote
0answers
35 views

Lecture notes on holomorphic Yang-Mills theory

Some time ago I've found these lecture notes on the gauge theory. In particular, in these lecture notes the author introduces and studies the Yang-Mills equations in the case of real bundles and ...
7
votes
1answer
108 views

Derivation of Schrödinger's equation

I recall a famous quote of the late physicist Richard Feynman: Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger. This ...
10
votes
2answers
185 views

Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ...
6
votes
1answer
188 views

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 ...
10
votes
3answers
246 views

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 ...
7
votes
6answers
250 views

Proving that $E=mc^2$

What are the axioms of special relativity? Is there a book or paper that introduces the theory of special relativity in a rigorous manner, and proves that $E=mc^2$ after appropriate definitions?
2
votes
1answer
104 views

Learning Advanced Mathematics

I'm a 12th grade student and I've recently developed a passion for mathematics . Currently my knowledge in this particular area is comprised by : single-variable calculus , trigonometry , geometry , ...
11
votes
6answers
1k views

Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
2
votes
0answers
205 views

Free lecture notes to Carl Bender's Mathematical Physics video lecture course?

I am just watching Carl Bender's Mathematical Physics video lecture course (about asymptotics and its application in physics) http://www.perimeterscholars.org/328.html which is great! Are there any ...
1
vote
0answers
37 views

Short examples that are/are not quantum-ergodic

Are there any considerably short examples of manifolds that are/aren't quantum ergodic, or quantum unique ergodic? Note that a (compact) Riemannian manifold is said to be quantum ergodic if ...
4
votes
5answers
606 views

What physics book for aspiring theoretical physicist / pure mathematician [closed]

I am a high school student. I want to learn physics on my own, but I am puzzled : Should I read a book which talks about all branches of physics? If yes, recommend a book. Should I read a book which ...
3
votes
1answer
162 views

Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”?

Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied ...
1
vote
3answers
81 views

Online resources for special relativity

I wasn't sure where to post this, but I'm on a mathematics course that has basically brushed over special relativity. I'm also doing an out of department module called philosophy of physics and as you ...
1
vote
1answer
45 views

E. Artin theorem? (Ergodic theory)

In the framework of mathematical cosmology, Bianchi IX model has great importance due to its stochastic properties. I'm reading a publication in which is claimed The use of the invariant measure ...
12
votes
4answers
486 views

Mathematical and Theoretical Physics Books

Which are the good introductory books on modern mathematical physics? Which are the more advanced ones? I already read Whittaker's Analytical Dynamics, and I am reading Arnold's Mathematical Methods ...
5
votes
1answer
93 views

What is Newton's theorem?

I'm reading a paper about mathematical physics at the moment and am wondering about the following: Let $w\colon\mathbb{R}^2\to\mathbb{R}$ be defined by $w(x)=-\log|x|$ and ...
12
votes
2answers
531 views

Mathematically rigorous text on classical electrodynamics.

Is there any textbook (preferably not written by a physicist) on classical electrodynamics which gives a rigorous (by the standards of pure mathematics) treatment of (a part of) the topics found in ...
4
votes
0answers
101 views

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 ...
2
votes
1answer
170 views

Looking for recommendations on textbooks for self study in a few subjects

I'm a first year graduate student in physics who picked up both an undergraduate degree in math and physics. However, in getting the math degree there were a few courses I either didn't take or ...
4
votes
6answers
264 views

Books for studying Mathematical Physics?

Currently I'm doing Advanced Classicial Mechanics courses.I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters. Can anyone ...
8
votes
1answer
486 views

Applications of representation theory in physics

The notes of a lecture on basic group and representation theory I attended last semester begin with a bit of motivation for the argument. They give the following examples for applications in physics: ...
5
votes
0answers
83 views

Second law of thermodynamics as a theorem about state space evolution

I once saw a mathematical explanation of the second law of thermodynamics. The statement was something like this: there is a mapping $f$ from the set of thermodynamic states $S$ to itself, and a ...
3
votes
0answers
76 views

The intuition behind a matrix of a Hamiltonian?

We have derived an elegant partition function for a problem which resembles a quantized model taking the particles to be Bosons. The related Hamiltonian for every $i$th ensemble is there: ...
3
votes
1answer
202 views

What is a good gentle introduction to the Virasoro algebra and its application in theoretical physics?

I am looking for an as gentle and pedagogical as possible introduction that explains the Virasoro algebra and its applications in theoretical physics; finally I am interested in its application in ...
4
votes
0answers
186 views

Rewriting the advection-diffusion equation

This is mostly a reference request question, although I certainly appreciate any insights and/or comments. Let us assume $p:R^n×(0,∞)\to \mathbb R$ is a scalar concentration, $u\in R^n$ is the ...
1
vote
0answers
34 views

Three body problem with point interactions

I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials). Is ...
1
vote
1answer
107 views

Translation of an article

I need to read this article "On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups" authors:G.Zhislin, A. ...
1
vote
0answers
28 views

References for three body problems with Fermi statistic

I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows them?
18
votes
3answers
458 views

Making some standard theoretical physics argument rigorous

In theoretical physics one often encounters the following rationale: if $f$ and $g$ are functions on $\mathbf{R}^n$, satisfying some technical conditions, and $\displaystyle\int_\Omega f=\int_\Omega ...
3
votes
0answers
67 views

Hyperbolic Motion in a Central Field

I have to give a 30 mins lecture this coming Thursday in my classical mechanics class (graduate level in math department, with Arnold as the primary text) and I am really struggling to find any good ...
1
vote
1answer
122 views

References for the HVZ theorem?

Is there someone who knows references for a proof of the HVZ theorem in the case of a system of $N$ particles, some of which are fermions?
4
votes
4answers
719 views

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 ...
2
votes
1answer
201 views

concise review of Maxwell's electromagnetic equations for math students

I am a graduate student in applied mathematics and I am looking for a concise introduction to Maxwell's equations / basic principles of electromagnetism. (I have enjoyed the book by Purcell, ...
4
votes
2answers
438 views

$SU(2)$ Representation of $SO(3)$

I've often seen it written that $SU(2)$ is a "two-valued representation" of $SO(3)$ (in theoretical physics books mainly). I have a major conceptual issue with this however. I know there is a Lie ...
1
vote
3answers
138 views

What do I need to read to understand dimensions and spacetime?

The concept of dimension seems to be: In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point ...
2
votes
1answer
198 views

Branch of Mathematics correlating with Physics

I am taking a course in physics -- intro to modern physics and physics 2 -- next semester, and the average weighted score, of people who took it in my university, is very low. I am wondering, ...
8
votes
5answers
438 views

Is there any abstract theory of electrical networks?

Designing electrical networks is among the highly mathematical engineering disciplines, which uses a vast scope of techniques from Fourier analysis and complex function theory, to logic, combinatorics ...
2
votes
1answer
169 views

Reference for topology and fiber bundle

I am looking for an introductory book that explains the relations of topology and bundles. I know a basic topology and algebraic topology. But I don't know much about bundles. I want a book that ...
5
votes
0answers
360 views

Min Max Principle and Rayleigh-Ritz-Method for eigenvalues of unbounded operators?

Finding eigenvalues of matrices using the Rayleigh-Ritz quotient is well-known, c.f. http://en.wikipedia.org/wiki/Min-max_theorem Does the following generalization of that fact also hold? Theorem: ...
1
vote
1answer
57 views

Question about Lie superalgebra.

What are the generators and relations for the Lie superalgebra $\mathfrak{psu}(2, 2 | 4)$? Thank you very much.
10
votes
0answers
465 views

What Areas Should a Potential String Theorist Study at Graduate Level? [closed]

Next October I start a year long course in Cambridge, intended as preparation for a PhD. I chose mainly pure disciplines as an undergrad (particularly topology and analysis) but I'd really like to ...