Questions tagged [field-theory]

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How to fix these warnings from an NDSolve code?

The following code works but it give several warnings that makes me feel nervous about the reliability and accuracy of the output: NDSolve: Warning: estimated initial error on the specified spatial ...
Cham's user avatar
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4 votes
1 answer
126 views

Why is there an error about division by 0?

I'm converting all of my old Mathematica 7.0 codes to my new Mathematica 13.2, and I'm struggling with some issues I didn't encounter with version 7.0. The following code is giving me a headache, ...
Cham's user avatar
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5 votes
1 answer
153 views

How to know which is value for field extension

I can convert $\sqrt{5}$ into a AlgebraicNumber: ToNumberField[Sqrt[5]] ...
yode's user avatar
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2 votes
1 answer
208 views

Field axioms in Mathematica

I don't understand the result of AxiomaticTheory["FieldAxioms", "Axioms"] ...
user64494's user avatar
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1 vote
1 answer
104 views

How can I do the same thing with mathematica? [duplicate]

I would like to do the same thing that we can see from the picture but with Mathematica. The problem is that I am only an high-school student which try to do this. It would be appreciated if it could ...
J.Doe's user avatar
  • 27
0 votes
1 answer
166 views

Minimal polynomial of an element in a polynomial quotient ring

Let $p(z)$ be a (not necessarily irreducible) polynomial in $\mathbb{Q}[z]$. Is there a built-in function I can use for determining the minimal polynomial of an element $\overline{q(z)} \in \mathbb{Q}[...
Feryll's user avatar
  • 101
2 votes
1 answer
124 views

Factoring a polynomial over a number field

Consider a polynomial x^3-x-1 and let $\alpha$, $\beta$, $\gamma$ be three zeros of the polynomial where $\alpha \in \mathbb{R}$. Since $\beta \not \in \mathbb{Q}[\alpha]$ and the degree of the ...
seoneo's user avatar
  • 185
0 votes
0 answers
86 views

Transforming a tensor expression

I have the expression $\qquad\sqrt{\det[\gamma^{\mu \nu} F_{\mu \nu}]}$ Basiclly, I need to expand this expression in some form like : $trF^4 + (trF^2)^2 + \sqrt{\det[F_{\mu \nu}]}$, where $\gamma^{\...
Mendrit Ljatifi's user avatar
2 votes
0 answers
376 views

How to define tensors similar to Riemann tensor in xAct xTensor xTras

I'm working on a project where we deal with objects very similar to Riemann tensor. In fact they are Christoffel symbols for higher spins. I'm using xTras for modeling problems in wolfram mathematica. ...
Melik Karapetyan's user avatar
4 votes
1 answer
1k views

How to compute functional derivative against vector in xAct, xTensor or xTras?

I want to compute the functional derivative against vectors. For example, I have an object that looks like this $R = h_{ijkl}a^i a^j a^k a^l$ I need to compute $\frac{\delta R}{\delta a^p}= 4 h_{...
Melik Karapetyan's user avatar
1 vote
0 answers
92 views

Derivatives with dummy indices not commutative after 3d derivative?

Recently I've encountered the following issue in xAct. I've defined the Manifold and tensors in the following manner Then consider the following expressions. In the case where there are 2 ...
Melik Karapetyan's user avatar
1 vote
0 answers
126 views

How to combine symmetrized tensor expressions into single expression in xAct

Let's sayI have the following expression in xAct where covariant derivatives are commutative, $\epsilon$ and $h$ are symmetric tensors. As we can see this expression is equivalent to If we ...
Melik Karapetyan's user avatar
3 votes
0 answers
106 views

How to speed up xTensor simplification?

I need to compute a variation of the 4th rang symmetric tensor. I've written a code that successfully computes it, but when I use the resulting tensor to compute the second variation the ...
Melik Karapetyan's user avatar
1 vote
1 answer
599 views

How to define commutative covariant derivatives in xTensor

I'm new with working xAct package and got stuck defining covariant derivatives that commute with each other. I want to simulate flat space-time. And here is my code ...
Melik Karapetyan's user avatar
0 votes
1 answer
229 views

Autocorrelated random field generation

Problem is related with my other question So, generate exponentially correlated row $π‘₯_{0,0},π‘₯_{1,0}...π‘₯_{𝑛,0}$ and starting from π‘₯0,0 there will be a correlated column $π‘₯_{0,1},π‘₯_{0,2}...π‘₯_{...
crx's user avatar
  • 87
2 votes
1 answer
445 views

NDSolve: method of lines: unexpected error: insufficient boundary conditions

As a test of my ability to master the Method of Lines I tried to NDSolve the PDE's system $$\partial_t \varphi = \varpi\qquad\partial_t\varpi=\frac{1}{r}\partial^...
dkstack's user avatar
  • 103
0 votes
1 answer
101 views

Need a package to compute constraint structure

I want to compute constraint structure of some field theory and some gravitational field theory. By constraint structure I mean what is explained in the "Lectures on Quantum Mechanics" by P. A. M. ...
physics portal's user avatar
0 votes
0 answers
58 views

How to define custom operator for working with tensors with multiple indices?

I've symmetric tensor $h(z)$ with rank $s$. Instead of writing symmetric tensor with its components I use the following notation $h^{(s)}(z;a) = \sum_{\mu_i}(\prod_{i=1}^{s}a^{\mu_i})h^{(s)}_{\mu_1\...
Melik Karapetyan's user avatar
5 votes
1 answer
256 views

Implementing the field axioms with FindEquationalProof?

I am fiddling around with FindEquationalProof, currently trying to prove some basic statements for fields. I have a set of axioms which almost constitutes the field theory axioms: ...
Michael L.'s user avatar