Questions tagged [field-theory]

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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^{\...
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49 views

Help with a custom coordinate transformation

I'm just starting to use Mathematica and can't wrap my head around the task I have at hand. It comes from field-theory. (Sorry I had to insert formulas as images instead of proper LaTex as it would ...
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0answers
79 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. ...
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1answer
358 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_{...
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41 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 ...
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0answers
41 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 ...
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0answers
69 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 ...
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1answer
227 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 ...
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1answer
124 views

Autocorrelated random field generation

Problem is related with my other question So, generate exponentially correlated row $𝑥_{0,0},𝑥_{1,0}...𝑥_{𝑛,0}$ and starting from 𝑥0,0 there will be a correlated column $𝑥_{0,1},𝑥_{0,2}...𝑥_{...
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1answer
261 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^...
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1answer
87 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. ...
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45 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\...
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1answer
189 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: ...