Questions tagged [mathematical-physics]
DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.
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Why does the finite trace of density matrix imply a discrete Schmidt decomposition? [closed]
In the paper defining an average Schmidt number for a particular entangled system, Law and Eberly say:
Because density matrices always have finite trace, the Schmidt decomposition is always discrete, ...
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What are the distinct mathematical formalisms of quantum mechanics?
Consider the physical theory called non-relativistic quantum mechanics. What are the distinct mathematical formalisms for this physical theory? That is, different mathematical frameworks for this ...
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Non-orientability in electromagnetism
I'm currently studying E&M and I have a question related to the mathematical formalism of the theory. Electrodynamics depends heavily on the divergence and Stokes's theorem which in their ...
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Concrete statement about QFT not being mathematically rigorous [duplicate]
It is often mentioned that QFT is ill-defined mathematically. I have seen this as stated that QFT can be defined on a lattice, but that it breaks down if the lattice spacing goes to zero. ...
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Elasticity theory: homogeneous deformations of a perfect lattice
I want to understand how the macroscopic (linear) elasticity theory emerges from the microscopic properties of matter. My question is about the model of the "perfect lattice", which is used ...
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Trouble understanding the experssion of gravity on a cube shaped earth
I'm a high school student working on a maths/geophysics project of which my goal is to try to mathmatically expressthe forces that apply on fluids, and then put them together to express geostrophic, ...
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Question about the identity operator and the bosonic ladder operators
Consider a self-adjoint operator $B$, such that for each mode $a_1,...,a_n$ [of a quantum bosonic system with Hilbert space $\cal H$ given by the corresponding Fock space] we have $B a_i B^\dagger = ...
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Determining Bound States from Møller Operator
Hello I came across an interesting property of the Møller operator, which I summarize below:
The Møller operator $\Omega^{(+)}$ maps in-states that belong to the continuum spectrum of the free ...
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Equivalent definitions of Wick ordering
Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
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Scattering matrix vs. unitary transformations
In quantum optics, the input/output bosonic modes at a beam splitter transform according to the scattering matrix
$$
\begin{pmatrix}
a_1 \\
a_2 \\
\end{pmatrix} = \dfrac{1}{\sqrt{...
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Multimode squeezed operator
Given CCR (bosonic) algebra, with creation / annihilation operators $a_{i}^{\dagger}, a_i$ acting on a single particle Hilbert space $\mathbb{h}$, let's introduce the multimode squeezed operator for $...
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Why does a singularity imply the need for a distribution?
I am following Section 11 of Prof. Etingof's MIT OpenCourseWare notes on "Geometry And Quantum Field Theory" in which he says:
...for $d = 1$, the Green's function $G(x)$ is continuous at $...
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When do two state functions represent the same quantum state?
According to the standard quantum mechanics, quantum states are one-dimensional subspaces of a separable Hilbert space. In practice, this Hilbert space is $L^2(M)$ where $M$ is the classical ...
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Correlation length in a 3d Ising slab with one dimension much smaller than the other two
Suppose I have a 3d Ising model on a cubic lattice, but one of its dimensions is much smaller than the other two. That is, I have an $L$ by $L$ by $L'$ slab with $L' << L$; in particular, $L'$ ...
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Why is $H = J \sum_i (S^x_i S^x_{i+1} + S^y_iS^y_{i+1})$ always gapless for any spin $S$?
In the following I have in mind antiferromagnetic spin chains in periodic boundary conditions on a chain of even length $L$.
Consider the spin-$S$ spin chain
$$H = J \sum_{i=1}^L (S^x_i S^x_{i+1} + S^...
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