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Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elementary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

"Mathematical physics consists of 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." (from Journal of Mathematical Physics). This tag is intended for questions on mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

Do not use just because your question involves physics!

See also Physics Stack Exchange's discussion on mathematical physics, Math Overflow's discussion on mathematical physics and Physics Overflow for further reference.

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What a reference frame is mathematically?

Physicists usually talk about reference frames and more specially inertial reference frames. This is particularly important in Mechanics and Relativity. Now, from the Physics standpoint there's no doubt on what is a reference frame: it is a point of…
Gold
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an object is rolling down a circular curve

An object is dropped from the top of a circular curve with radius r and rolls down the curve until it reaches the bottom. What would be the equation that would give the velocity of the object at any given time? Assume that the gravity of earth is…
Jacob
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What is mathematical equation of the Gravitational force between three objects?

This is mathematical equation of the Gravitational force between two objects: $$F_G=\frac{GM_1M_2}{r^2}$$ what is mathematical equation of the Gravitational force between three objects?
Ahmad
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Inverse Proportionality

Inversely proportional: $ab = K$ where $a$ and $b$ are variables and $K$ is the constant of inverse proportionality (?). So, if $a$ increases/decreases, $b$ decreases/increases. Neat! $x + y = K$. $x$ and $y$ are variables and $K$ is a constant.…
Agent Smith
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Problem in Newton's Principia mentioned by V. I. Arnol'd

In an article named Conversation with Vladimir Igorevich Arnol'd, Arnol'd said I will state another problem mentioned there, this one variational, on the solid of revolution with least resistance under motion along its axis in a very rarified…
J_KI
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Multiplying two Scalar dot products together

stackexchange community, I'm just wondering what the rules are for multiplying dot products together, such as: $$ (P_{3}\cdot{P_{4}})(P_{1}\cdot{P_{2}}) $$ How would this be expanded out to not contain any dot products?
Michael Roberts
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Inclined plane - euler-lagrange

A mass point of mass m moves frictionlessly down an inclide slope under influence of gravity. Solve the equations of motion and determine the constraint with the use of the lagrange equation of second kind. I'm learning for my upcoming exam and…
Rab
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Is $\nabla$ a vector?

The following passage has been extracted from the book "Mathematical methods for Physicists": A key idea of the present chapter is that a quantity that is properly called a vector must have the transformation properties that preserve its…
Sensebe
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Does Lagrangian always exist for any equation?

In mathematical physics, a lot of equations can be interpreted as a solution of least action principle for some Lagrangian. I wonder if for every equation there is a Lagrangian so that one achieves the original equation when solving the principle of…
Henry
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Complex charge in RLC circuit

Calculate the absolute value of the complex charge in the RLC circuit: $$Q(t)=\frac{V_0e^{i\omega t}}{-\omega^2L+i\omega R+\frac{1}{c}}.$$ Find the frequency where $|Q(t)|$ is maximum. This question is from Mathematical methods, by Boas. I am…
Robben
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Can you prove $F=ma$ mathematically?

So, it is one of Hilbert's famous problems to "axiomatize physics". In these attempts to establish physics as a subfield of mathematics, I wonder where does the Newton's law $F=ma$ stand. To be more specific, I ask the following questions. (1)…
a12345
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Special Relativity Dilation problem

I've been given the following scenario: Observer $B$ is in the center of a train carriage which is moving at velocity $v$ with respect to an observer $A$. Two light signals are emitted from sources L at the left end and R at the right end of the…
Lammey
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Definition of Feynman diagram

I'm reading Costello's book "Renormalization and effective field theories" (preliminary PDF, p. 35). I am stuck on his discussion of Feynman diagrams. He considers a finite-dimensional super vector space $U$ and the completed symmetric algebra…
fresh
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How do I calculate the following? (with answers)

Would anyone be able to help me calculate the following questions? I have the answers, I just want to understand the process. If you are able to give me any feedback, would you be able to write your answer in simple steps plugging in the values?…
Alexis Maria
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Equivalence between mathematical and physical definition of a tensor

I want to understand how the "physicists' definition" of a tensor and the "mathematicians' definition" are equivalent. I'm going to stick to the finite dimensional case, and note that I am not concerned with the difference between tensor fields and…
Jbag1212
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