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Questions tagged [field-theory]

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1 answer
54 views

Solving PDEs In Tensor Form

I have a set of field equations (PDEs) expressed tensor form that I derived using xAct and xTensor. Is there any function that would allow me to put the full tensor form of the field equations as an ...
3 votes
1 answer
234 views

Field axioms in Mathematica

I don't understand the result of AxiomaticTheory["FieldAxioms", "Axioms"] ...
2 votes
2 answers
132 views

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 ...
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, ...
5 votes
1 answer
156 views

How to know which is value for field extension

I can convert $\sqrt{5}$ into a AlgebraicNumber: ToNumberField[Sqrt[5]] ...
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 ...
0 votes
1 answer
192 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}[...
2 votes
1 answer
129 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 ...
0 votes
0 answers
87 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^{\...
2 votes
0 answers
384 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. ...
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_{...
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: ...
1 vote
0 answers
95 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 ...
1 vote
0 answers
131 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 ...
3 votes
0 answers
108 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 ...
1 vote
1 answer
622 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 ...
0 votes
1 answer
234 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‘₯_{...
2 votes
1 answer
459 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^...
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. ...
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\...