What is Mathematical physics: Definition and 241 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".
I am planning on pursing a Phd in Theoretical physics or Mathematical Physics in the next several years. My main motivation is doing research when it comes to grand unified theory. What areas of research (within that umbrella, in a theoretical sense) should I start looking into that are at the...
(To moderators: although the question is mathematical, I post it in the physics forum because the definition and the notation are those used by physicists and because it comes from a QFT textbook; please move it if I'm wrong.)
My issue with this question is that the textbook has neither defined...
Hello,
Which is the best beginner friendly mathematical physics book that can help me understand undergraduate physics? I'm self teaching myself from the videos. Right now I've learnt upto higher school mathematics(trigonometry, calculus, vector algebra and matrices).
Hey,
I have a question regarding the gluons. Is it possible for a non-commutative group/geometry to represent them mathematically ? Replacing the Gell-Mann matrices. I read that the frameworks for gluons /gluonic forces are various, depending on the context.
I have been reading Mathematical Physics from Marl L. Boas' `Mathematical Methods in the Physics Sciences` and it's ok. But, I feel like for someone who hasn't been exposed to topics like Fourier Series, I need greater context. I feel like I should have chosen a different book, but that's...
Dear everyone,
I'm an HDR student in Condensed Matter Physics. I want to enhance my math ability with the aim is learning physics.
I found two books, they seem all fit my purpose.
1. Mathematical Physics 2nd by S.Hassani
2. Physical Mathematics 2nd by K.Cahill
I want to choose one of them to...
This question comes from my experience in radar signal processing. As I am going more deep into the theory of sampling, statistical signal processing and estimation theory in general, I have a very silly but important mathematical question that I want to ask here.
For example, we are estimating...
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 :
-...
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...
I finished my 1st-year physics, took analysis, linear algebra, mathematical logic, classical mechanics, quantum mechanics(I was exempted from intro phy and took some 3rd-year physics courses)
I internal transferred to pure maths. The reason is that the curriculum of the physics programme in our...
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...
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...
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...
(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...
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...
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...
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...
A post doc in an area that differs from my PhD?
I am currently doing a PhD in fluid mechanics but want to do mathematical physics tbh. In another thread I got an answer about a user who had done a PhD in accelerator physics and went to do a post-doc in condensed matter, vice versa even, but in...
I am reading his excellent book "Mathematical Physics Part 1, Second Edition", which has benefited me a lot in many ways.
However, I have a doubt about the correctness of the theorem 2.3.23, which states that for any subspace U of V, the map T ' : V/U -> T(V) defined by T ' ([a]) = T|a> is...
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...
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}...
Hey everyone, I am a new member. This post is about something that bothers me a lot and will affect my future. I am not sure whether I'm pursuing a carrer that is right for me.
I graduated from the physics department of Middle East Technical University in Turkey with 3.45/4.00 CGPA this year...
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) =...
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...
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...
Do Holographic Screens eliminate the need of finding holographic dualities?
There are various models in physics based on the famous holographic principle (https://en.wikipedia.org/wiki/Holographic_principle)
This does not always work since in these models we must find a correlation between two...
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...
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...
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'}...
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.
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...
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...
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...
Homework Statement
Calculate
\int_{S} \vec{F} \cdot d\vec{S} where
\vec{F} = z \hat{z} - \frac{x\hat{x} + y \hat{y} }{ x^2 + y^2 }
And S is part of the Ellipsoid x^2 + y^2 + 2z^2 = 4 , z > 0 and the normal directed such that
\vec{n} \cdot \hat{z} > 0
Homework Equations
All the...
Homework Statement
Calculate the integral
\int_{S} (\frac{A}{r^2}\hat{r} + B\hat{z}) \cdot d\vec{S}
Where S is the sphere with r = a.
2. The attempt at a solution
I have no clue how to solve this problem. I have thought of introducing spherical coordinates and somehow finding a connection...
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...
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}...
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...
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...
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...
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...
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...
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...
Hey.
Undergrad UK Chemical Physics student here. Looking for some advice when it comes to sorting out my degree path.
First however. Some background info for those unaware with the degree 'system' in the United Kingdom:
Most Universities in the UK have you apply for degree programs through...
Homework Statement
Homework EquationsThe 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...
Homework Statement
Homework EquationsThe 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 as...
Homework Statement
Homework EquationsThe 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...