Mathematical physics Definition and 74 Discussions

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".

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  1. kafka64

    Courses Should I skip labs/experiments for Mathematical Physics program?

    I am attending University of Waterloo and my school will allow me to graduate as a Mathematical Physics major without taking any labs/experiment courses (in my school lab is not integrated to physics courses, they are separate courses with separate credits). This could be great because : -...
  2. S

    Deciding between physics and mathematics

    I am not sure if this is the right place to post this, so if not sorry in advance. I am a second-year physics major, thinking of switching to mathematics. I have always been interested in both, but I could never be sure whether I could become a mathematician. Understanding physics was...
  3. Introduction/Logic of propositions and predicates- 01 - Frederic Schuller

    Introduction/Logic of propositions and predicates- 01 - Frederic Schuller

    This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller
  4. warhammer

    Fourier Transforms -- Please check my solution

    My Professor has started on the Fourier Transforms Topic in the Introductory Mathematical Physics class and gave us a small homework to try our concepts on. I have attached a clear & legible snippet of my solution. I request someone to please have a look at it & determine if my solution is...
  5. M

    Studying Should I study Topology or Group Theory?

    Hello! I'm a physics graduate who is interested to work in Mathematical Physics. I haven't taken any specialized maths courses in undergrad, and currently I have some time to self-learn. I have finished studying Real Analysis from "Understanding Analysis - Stephen Abbott" and I'm currently...
  6. ipsky

    Intro Physics Opinions on books for (self) studies in statistical physics

    Nearly two decades after I graduated with an engineering degree, I'm currently studying for a master's with a particular emphasis on conceptual/theoretical statistical physics. Based on my interests and stylistic preferences, I'm using the following books to build my understanding of physical...
  7. warhammer

    Other Need guidance please for purchasing a textbook on Math Physics

    (EDIT: I have also added 2 snippets of the syllabus of the entire Math Physics course in my curriculum as reference). I am currently in the 3rd Semester of my 3 year UG Physics degree from where the subject of Math Physics has been separately included. I need extensive guidance from someone...
  8. W

    Studying Physics intrigues me but Math makes more sense. What to study?

    Hi, I have the following problem, maybe someone relates. I am about to finish my Bachelors Degree in Physics and must say it was a very unenjoyable road. I started it because since forever I was fascinated by the "great" ideas trying to explain reality that lie behind physics, i. e. Quantum...
  9. Tianluo_Qi

    Quantum Reading list recommendation for HEP-ph to HEP-th/math-ph transition

    One sentence summarization For a student initially working on a more phenomenological side of the high energy physics study, what is the recommendation of introductory reading materials for them to dive into a more mathematically rigorous study of the quantum field theory. Elaboration...
  10. XCodeX

    Cosmology Physics book suggestions

    Hi All. It is my first post here. I am PhD student studying algebraic/complex geometry. I am very interested in mathematical physics. I am currently enrolled in two courses in coursera electrodynamics and thermodynamics. Can someone suggest what courses I should enrol in or study plus books ? I...
  11. S

    Coarsest and finest topology

    I do not understand what is to verify here. The problem already defined what it means to be a trivial and discrete topology but it did not state what it means to be "weak" and "strong". I assume the problem wants me to connect "weak" with trivial topology and "strong" with discrete topology, but...
  12. V

    I Riemannian Fisher-Rao metric and orthogonal parameter space

    Let ## \mathcal{S} ## be a family of probability distributions ## \mathcal{P} ## of random variable ## \beta ## which is smoothly parametrized by a finite number of real parameters, i.e., ## \mathcal{S}=\left\{\mathcal{P}_{\theta}=w(\beta;\theta);\theta \in \mathbb{R}^{n}...
  13. A

    A Problem understanding these concepts in Jackson

    In Jackson, (3rd edition p. 545), there are equations they are given as, $$A = e^L $$ $$det A = det(e^L) = e^{Tr L}$$ $$g\widetilde{A}g = A^{-1} $$ $$ A = e^L , g\widetilde{A}g = e^{{g\widetilde{L}g}} , A^{-1} = e^{-L}$$ $$ g\widetilde{L}g = -L $$ I have several doubts. 1) $$det(e^L) =...
  14. L

    A Unitary representations of Lie group from Lie algebra

    In Quantum Mechanics, by Wigner's theorem, a symmetry can be represented either by a unitary linear or antiunitary antilinear operator on the Hilbert space of states ##\cal H##. If ##G## is then a Lie group of symmetries, for each ##T\in G## we have some ##U(T)## acting on the Hilbert space and...
  15. M

    Conservation laws in Newtonian and Hamiltonian (symplectic) mechanics

    In Newtonian mechanics, conservation laws of momentum and angular momentum for an isolated system follow from Newton's laws plus the assumption that all forces are central. This picture tells nothing about symmetries. In contrast, in Hamiltonian mechanics, conservation laws are tightly...
  16. S

    A Do Holographic Screens eliminate holographic dualities?

    Do Holographic Screens eliminate the need of finding holographic dualities? There are various models in physics based on the famous holographic principle ( This does not always work since in these models we must find a correlation between two...
  17. STasnim12357

    Schools How good is the Theoretical Physics MSc course at Queen Mary?

    Hello am currently an undergraduate student. My major is CSE. But I am very much interested to do my masters and then PhD in theoretical physics/mathematical physics. Is there any university that admits CS graduates for these courses? I have looked up some universities that offer these courses...
  18. M

    I Why is there a contradiction?

    Let: ##\nabla## denote dell operator with respect to field coordinate (origin) ##\nabla'## denote dell operator with respect to source coordinates The electric field at origin due to an electric dipole distribution in volume ##V## having boundary ##S## is: \begin{align} \int_V...
  19. M

    I Showing that B has no discontinuities at the surface

    Consider a magnetic dipole distribution in space having magnetization ##\mathbf{M}##. The potential at any point is given by: ##\displaystyle\psi=\dfrac{\mu_0}{4 \pi} \int_{V'} \dfrac{ \rho}{|\mathbf{r}-\mathbf{r'}|} dV' + \dfrac{\mu_0}{4 \pi} \oint_{S'}...
  20. Gursimran Singh

    Potential energy of a shell and a disc, both covered uniformly with charge

    Double integration maybe?? I calculated potential due to shell on plate's center but not on other points on it's surface.
  21. The Big Bang, Cosmology part 1: Crash Course Astronomy

    The Big Bang, Cosmology part 1: Crash Course Astronomy

    Thanks to observations of galaxy redshifts, we can tell that the universe is EXPANDING! Knowing that the universe is expanding and how quickly its expanding also allows us to run the clock backwards 14 billion years to the way the universe began - with a bang.
  22. L

    A Interpretation of state created by the field in free QFT

    Let us consider QFT in Minkowski spacetime. Let ##\phi## be a Klein-Gordon field with mass ##m##. One way to construct the Hilbert space of this theory is to consider ##L^2(\Omega_m^+,d^3\mathbf{p}/p^0)## where ##\Omega_m^+## is the positive mass shell. This comes from the requirement that there...
  23. Auto-Didact

    A PDE: Between Physics and Mathematics

    This is perhaps the single most important mathematical physics papers I have ever read; I think everyone - especially (theoretical) physicists - interested in theoretical physics should read it. In fact, read it now before reading the rest of the thread: Klainerman 2010, PDE as a Unified Subject...
  24. A

    Programs Mathematical physics

    I am currently an undergrad in pure Math. Until now, the courses I found the most fun/interesting were Probability 1&2, Geometry and Group Theory. I still have 3 semesters to go. Prior to math I did some university courses in physics which were Classical Mecanics1, Optics and Intro to modern...
  25. A

    I Verifying an equality

    I have an expression ##\mathcal{Im}[RT^*e^{-2ip}]=|T|^2\sin p ##, where ##R=Ae^{ip}+Be^{-ip} ## and ##p ## is a real number. This ultimately should lead to ##\mathcal{Im}[A+B+Te^{2ip}]=0 ## upto a sign (perhaps if I didn't do a mistake). There is a condition on ##R ## that it is real...
  26. Pushoam

    Dimensionality of the sum of subspaces

    Homework Statement Suppose that ## \mathbb {V}_1^{n_1} ## and ## \mathbb {V}_2^{n_2} ## are two subspaces such that any element of ## \mathbb {V}_1^{n_1} ## is orthogonal to any element of ## \mathbb {V}_2^{n_2} ## . Show that dimensionality of ## \mathbb {V}_1^{n_1} + \mathbb {V}_2^{n_2}...
  27. Pushoam

    Schwarz inequality

    Homework Statement For x,y,z ## \in \mathbb {R^+} ##, prove that ## \sqrt {x (3 x +y) } + \sqrt {y (3y +z) } + \sqrt {z(3z +x)} \leq ~ 2(x +y+ z) ## Homework Equations The Attempt at a Solution I don't know which inequality among the above two has to be applied. I am trying to solve it by...
  28. A

    Theoretical Physics should belong in the math department

    Theoretical Physics should belong in the math department to then collaborate with the physics department on new mathematical theories within physics. I can't accept that theoretical physics could really be considered a branch of just physics. I can only see theoretical physics being 95% math and...
  29. A

    A Rigorous transition from discrete to continuous basis

    Hi all, I'm trying to find a mathematical way of showing that given a complete set $$\left |a_i\right \rangle_{i=1}^{i=dim(H)}∈H$$ together with the usual property of $$\left |\psi\right \rangle = ∑_i \left \langle a_i\right|\left |\psi\right \rangle\left |a_i\right \rangle ∀ \left...
  30. L

    A Can disjoint states be relevant for the same quantum system?

    In the algebraic approach, a quantum system has associated to it one ##\ast##-algebra ##\mathscr{A}## generated by its observables and a state is a positive and normalized linear functional ##\omega : \mathscr{A}\to \mathbb{C}##. Given the state ##\omega## we can consider the GNS construction...
  31. Giulio Prisco

    A Did nature or physicists invent the renormalization group?

    Or in other words: The renormalization group is a systematic theoretical framework and a set of elegant (and often effective) mathematical techniques to build effective field theories, valid at large scales, by smoothing out irrelevant fluctuations at smaller scales. But does the...
  32. L

    A States in usual QM/QFT and in the algebraic approach

    Studying QFT on curved spacetimes I've found the algebraic approach, based on ##\ast##-algebras. In that setting, a quantum system has one associated ##\ast##-algebra ##\mathscr{A}## generated by its observables. Here we have the algebraic states. These are defined as linear functionals...
  33. Pushoam

    Line integral of a curve

    Homework Statement Homework Equations The Attempt at a Solution Line integral of a curve ## I = \int_{ }^{ } yz dx + \int_{ }^{ } zx dy + \int_{ }^{ } xy dz ## with proper limits. ## I = \int_{\frac { \pi }4}^{ \frac { 3 \pi} 4} abc ( \cos^2 t - \sin^2 t ) dt = -abc ## |I| = abc...
  34. Pushoam

    Solving 2nd order differential equation

    Homework Statement Homework Equations The Attempt at a Solution For the homogeneous equation, I have got the the root of the characteristic equation as ## e^{ix}, e^{-ix} ## . So, the corresponding solution is ## B \sin{ x} + A \cos{ x} ## . Then, I took the particular solution...
  35. Pushoam

    Graph of ##\sin(\sinh x)##

    Homework Statement Homework Equations The Attempt at a Solution ## \sinh (x) ## is continuous. ## \sin{( \sinh (x))} ## should have the same amplitude. ...(1) Option (a) and (b) follow this condition. For x = 0, ## \sin ({ \sinh (x)} ) ## = 0. ...(2) Option (a ) follows...
  36. Pushoam

    Determinant of exponential matrix

    Homework Statement Homework Equations The Attempt at a Solution [/B] Det( ## e^A ## ) = ## e^{(trace A)} ## ## trace(A) = trace( SAS^{-1}) = 0 ## as trace is similiarity invariant. Det( ## e^A ## ) = 1 The answer is option (a). Is this correct? But in the question, it is...
  37. fresh_42

    I Open problems in mathematical physics

    I came across this beautiful pearl which I like to bring to notice. Despite of its title it is heavier on theoretical physics than it is on mathematics, so I placed it in this forum. I think it is equally interesting to those...
  38. J

    Applied Zee and Georgi Group Theory books

    Hello. I will be attending a course on Group theory and the book that the professor suggests is Georgi's Lie Algebras in Particle Physics. As I liked Zee's book on General Relativity, I thought that it would be a blast to also use his Group theory textbook for the course. Problem is that I don't...
  39. Q

    Programs Master in theoretical/mathematical physics. Guidance.

    Hello, I was wondering if you could give me some advice on what master’s degree or which specific master courses I should take. I am a physics student and I am going to finish my bachelor in physics next year. I plan to do a master in theoretical physics or in mathematical physics. However I...
  40. Eslam100

    Other What are the topics in theoretical and mathematical physics?

    I'm a rising physics sophomore at a Japanese university. I've studied general physics, linear algebra, and analysis (actually, calculus of single and several variables with emphasis on analysis, everything was proven and the theoretical background was well explained) Other than that, I've...
  41. M

    I GR for a mathematician and a physicist? What's the difference?

    Have members of the community had the experience of being taught GR both from a mathematical and physics perspective? I am a trained mathematician ( whatever that means - I still struggle with integral equations :) ) but I have always been drawn to applied mathematical physics subjects and much...
  42. AXidenT

    Programs Advice on Graduate Studies in Mathematical Physics

    I recently completed my honours degree in Australia (4-year undergraduate with a year-long thesis and some grad-level subjects such as first courses in algebraic geometry, algebraic topology, GR, QFT and integrable systems) and am struggling to figure out what the best option for graduate study...
  43. J

    Courses String Theory and Theoretical vs. Mathematical Physics

    Hello, I have a question about the the difference between mathematical physics and theoretical physics in general and about the difference between the MSc Theoretical and Mathematical Physics courses at Edinburgh in particular. I am planning to apply, however I am not sure which of the two...
  44. Indiana

    Applied Which is more mathematical?

    Which is more mathematical among The Princeton Companion to Applied Mathematics and Mathematics for Physics by Michael Stone and Paul Goldbart? Both of them are applied mathematics books. What are the main differences between them? Which is more mathematical i.e. mathematically advanced...
  45. B

    Other Seeking "Reference" Textbooks in Mathematical Physics

    Dear Friends, Could you suggest me some good textbooks in the mathematical physics that I can use for both studying and reference? I am currently reading Landau/Lifshitz' trilogy along with couple other books (Weinberg for gravity, Arnold, etc) in different branches of physics, and I need to...
  46. Liam Lau

    Courses Mathematical Physics or Theoretical Physics

    Hi, I am currently applying to university and am an aspiring Theoretical Physicist. I see many different courses but the two I am not sure on are Mathematical Physics and Theoretical Physics. I was wondering what would give me a better foundation to go on to be a Theoretical Physicist, thank...
  47. J

    Particle Group Theory book for Undergraduates

    Hello, what are some good books to learn group theory for physicists at an undergraduate level? Is Zee's Group Theory in a Nutshell good? Thanks in advance
  48. P

    Programs What Physics degree would be best for me?

    I like physics because of the formulas, explaining nature in terms of maths (I love math), I love problem solving and it's just so diverse. You learn about subjects from materials to astronomy it's just learning about how stuff works. So topics I like: Kinematics Any mechanics Electricity...
  49. J

    Applied Mathematics for physicists books (poll)

    Hello, i want to get a mathematics book for physicists, and i have stumbled across some good books, but as i have not read them yet, i can't really decide which one to buy. So, which one do you prefer and why? Also, do you have any other book to recommend? Thanks!
  50. J

    Studying Guidance regarding Mathematical Physics

    Hello all, I've done an MSc in Physics alongwith a BE in Electronics Engg, graduating in 2014. My scores are quite poor (GPA: 6.23/10), but I am interested in doctoral studies in Mathematical Physics. I wrote exams for PhD admissions here in India for this year but did not fare well enough for...