## trouble with Levi-Civita symbol from physics-packa...

Hi, there!

I try to simplify the next expression:

Simplify(LeviCivita[4, sigma, lambda, rho]*LeviCivita[4, xi, eta, mu]*g_[rho, mu]*qp[sigma]*q[lambda]*qp[xi]*q[eta])

In reality it is incorrect answer, because indices must run over 1,2,3 but not 1,2,3,4!

SumOverRepeatedIndices(%) confirms that maple mistakes.

my preamble is:

with(Physics)

Setup(mathematicalnotation = true); Coordinates(X);

Setup(spaceindices = lowercaselatin)

Setup(tensors = q[mu](X))

PDEtools:-declare(q(X))

Setup(tensors = qp[mu](X))

PDEtools:-declare(qp(X))

## How can I see a list of the metric accepted in the...

I would like to see the list of metrics recognize by Maple with their acornym.  For example,:

>Setup(coordinates = spherical, metric = kerr)

## Error, (in unknown) invalid subscript selector...

Hello everyone, I use physics package and I input:

with(Physics)

Setup(mathematicalnotation = true)

Coordinates(X)

Setup(tensors = A[mu](X))

PDEtools:-declare(A(X))

PDEtools:-declare(p0(X), pm(X), pp(X), pt(X), Un(X), Ucn(X))

pt := proc (X) options operator, arrow; Matrix(2, 2, [[p0(X), sqrt(2)*pp(X)], [sqrt(2)*pm(X), -p0(X)]]) end proc

U := proc (X) options operator, arrow; Matrix(2, 2, [[1, 0], [0, 1]])+I*pt(X)*(1/f)-pt(X)*pt(X)*((1/2)/f^2) end proc

Ucn := proc (X) options operator, arrow; Matrix(2, 2, [[1, 0], [0, 1]])-I*pt(X)*(1/f)-pt(X) . pt(X)*((1/2)/f^2) end proc

And after that I write:

Trace(-LeviCivita[mu, nu, rho, sigma] . Ucn(X) . ((1/6)*e*A[nu](X)+M5*KroneckerDelta[nu, 0]) . Matrix(2, 2, [[1, 0], [0, 1]]) . Uсn(X) . d_[rho](Un(X)) . Uсn(X) . d_[sigma](Un(X)))

But I get an error:

Error, (in unknown) invalid subscript selector

Thanks for the help.

## Matrices in Physics package...

Hello! I try to make friends physics package and matrixes. But I am faced with difficulties. To be more specific, to consider a code:

with(Physics):
Setup(mathematicalnotation = true); Coordinates(X); Setup(tensors = A[mu](X)); PDEtools:-declare(A(X), p0(X), pm(X), pp(X), pt(X), U(X), m5(X))

And then I create a matrix:

pt := proc (X) options operator, arrow; Matrix(2, 2, [[p0(X), sqrt(2)*pp(X)], [sqrt(2)*pm(X), -p0(X)]]) end proc;

It displays as:

Why do p0, pp, pm become function only one variable x1?

Interestingly that maple understands the next matrix:

Nevertheless even for function only one variable derivative works fine:

And I can construct more complicated functions:

But why is only one variable?

## How to define a metric tensor in 3-d (r, theta, p...

Helle everybohy,

I need to setup a metric tensor in 3-d but with the varalble r, and .  So I try this:

>with(Physics); Setup(mathematicalnotation = true, dimension = 3)

>Setup(coordinates = spherical[r, theta, varphi], metric = M)

where M is the metric that I need to use.  But the last command does not work.  Il I don't write [r, theta, varphi], it work but it's r, theta and t.

Mario Lemelin

mario.lemelin@cgocable.ca

## How to do symbolic calculation in GR...

Hello everybody,

In the linearised theory of gravity, I want to do some symbolic calculations.  First, I need to set that:

Then I want to see how the Christoffel symbols will change by putting the above in this:

Any hint someone?  I really appreciate the help for learning the Physics package.  Thank you in advance.

Mario

## problem with multiplication ...

I need yours hepl.  I work with the physics paсkage and I set:

with(Physics)

Setup(mathematicalnotation = true)

Coordinates(X)

Setup(Dgammarepresentation = standard)

Setup(spaceindices = uppercaselatin)

Define(m, m5, y, p, mm, pp)

I try to square the next value:

W := Dgamma[mu]*d_[mu]+M+Psigma[A]*aa[A]-mm*Dgamma[0]-m5*Dgamma[0]*Dgamma[5]+I*Dgamma[5]*Psigma[B]*pp[B]+I*Dgamma[5]*y

("*" is multiplication)

W*W

And after that I want to simplify it:

Simplify(W*W)

I guess that matter is owing to d_[~mu]. If I remove this term:

E:=Psigma[A]*aa[A]-mm*Dgamma[0]-m5*Dgamma[0]*Dgamma[5]+I*Dgamma[5]*Psigma[B]*pp[B]+I*Dgamma[5]*y

And if i do:

E*E

Then next error emerges:

What is it?

## Hermitian conjugate ...

I need yours hepl.  I work with the physics paсkage and I set:

with(Physics)

Setup(mathematicalnotation = true)

Coordinates(X)

Setup(Dgammarepresentation = standard)

Setup(spaceindices = uppercaselatin)

Define(M, aa, mu, mu5, Pi, eta)

M_[mu, mu5] := Dgamma[mu]*d_[mu]+M+Psigma[A]*aa[A]-mu*Dgamma[0]-mu5*Dgamma[0]*Dgamma[5]+i*Dgamma[5]*Psigma[B]*Pi[B]+i*Dgamma[5]*eta

And next:

Dagger(M_[mu, mu5])

How is Maple explained that

Dagger(d_[mu])=d_[mu]

conjugate(M)=M

conjugate(aa[A])=aa[A]

conjugate(i)=i

and so on?

## Help in add / sum...

Hello, I need help in add/sum, there are two problems:

1. How we write triple summation (sigma) in Maple? (See pic)

2. How we write summation like in this pic?

for e from 1 to 9 do

for k from 1 to 17 do

if i=(2*e-1) then next else

end if

end do

end do

For example, the expected result for e=2 and k=1 is like following equation:

x[2,1,1]+x[2,3,1]+x[2,4,1]+x[2,5,1]+...+x[2,17,1]+x[2,18,1]=1

But the result I get:

x[2,1,1]+x[2,2,1]+x[2,3,1]+...+x[2,18,1]=1

How to omit the x[2,2,1]?

Thank you.

## Possible to work with Riemann Normal Coordinates i...

I would like work in Riemann Normal Coordinates, and derive expansion in number of derivatives of the metric.

For example, starting with the expansion of the metric in Riemann Normal Coordinates (assuming this needs not be derived)

$\displaystyle \begin{array}{rcl} g_{ij}(x)&=& \delta_{ij} -\frac 1 3 R_{iklj}x^kx^l -\frac 1 6 R_{iklj;m} x^kx^lx^m\\ &&+ (\frac2{45} R_{ilmk}R_{jpqk}- \frac 1 {20} R_{ilmj;pq})x^lx^m x^p x^q\\ &&+(-\frac 1{90} R_{iklj;mpq}+\frac 2{45} R_{iklr;m}R_{jpqr})x^kx^lx^mx^px^q\\ && +(-\frac 1 {504}R_{iklj;mpqr}+ \frac{17}{1260}R_{ikls;pq}R_{jmps}+ \frac{11}{1008}R_{ikls;q}R_{jmps;r}\\ && +\frac 1{315}R_{ilms}R_{jqrt}R_{kspt})x^kx^lx^mx^px^qx^r +O(|x|^7). \end{array}$

I would like to express the lapliacian, or square-root of the determinant ... etc., in terms of this metric and derive an expansion for them.

However, I cannot even define the metric as such in Maple-Physics, because the coefficients of xk depend themselfs upon the metric to be defined.

Is there a way to do such calculations in Maple ?

## bizarre bug in Physics tensor manipulation...

Here's a short tensor manipulation which goes totally bananas. Basically I have a metric, and I define a vector k, and right at the end I calcualte the covariant derivative of it. In the metric and elsewhere I have a constant epsilon, a function of time a(t), and 2 functions of all coords, Phi and psi. Then at the end it gives the covariant derivative of k, but now with epsilon and a as functions of all coordinates.

Any idea what's going on??

code:

restart;
with(Physics);with(PDEtools):
Setup(coordinatesystems=spherical);

ds2:=expand(a(t)^2*(-(1+2*epsilon*Phi(r,theta,phi,t))*dt^2+(1-2*epsilon*psi(r,theta,phi,t))*(dr^2+r^2*dtheta^2+r^2*sin(theta)^2*dphi^2)));
declare(%,(H)(t),(k0,k1,k2,k3)(X));
Setup(metric = ds2);

Define(k[~mu]=[-1/a(t)^2+epsilon*k1(X),epsilon*k2(X),epsilon*k3(X),1/a(t)^2+epsilon*k0(X)]);

Define(NullGDE[nu]=(k[~mu](X)*D_[mu](k[nu](X))),OpticalDeformationMatrix[mu,nu]=(D_[mu](k[nu](X))));

(OpticalDeformationMatrix[1,1,nonzero]);

the final output is Matrix(1, 1, [[(-(2*((diff(epsilon(X), r))*(psi(X))(X))+2*epsilon(X)*(diff((psi(X))(X), r)))*(epsilon(X)*(k1(X))(X)*((a(t))(X)^2)-1)*a(t)-(2*epsilon(X)*(psi(X))(X)-1)*((diff(epsilon(X), r))*(k1(X))(X)*((a(t))(X)^2)+epsilon(X)*((diff((k1(X))(X), r))*((a(t))(X)^2))+2*epsilon(X)*(k1(X))(X)*(a(t))(X)*(diff((a(t))(X), r)))*a(t)+epsilon*psi[r]*(epsilon*k1(X)*(a(t)^2)-1)*a(t)-epsilon^2*psi[theta]*(a(t)^3)*k2(X)-epsilon^2*psi[phi]*(a(t)^3)*k3(X)-(2*(diff(a(t), t))*psi(X)*epsilon+psi[t]*a(t)*epsilon-(diff(a(t), t)))*(epsilon*k0(X)*(a(t)^2)+1))*(1/a(t))]])

where epsilon is now a function!

## Physics courses that use the Maple Physics Package...

I apologize because this is not a technical question but I believe that the question and issue that I have is probably of interest to a wide range of Maple users.   I am a retired biophysicist and have been using Maple as a tool in my research since Maple 5.  I recently became aware of the amazing Maple Physics Package.  It seems to offer an incredible advance.  I say “seems” because its notation and complexity is a bit overwhelming.  What I was hoping to find was a complete course (or courses) in physics that used this package.  I was hoping that with such a course I could go through it in detail and could relearn physics and become proficient in using the package.  Unfortunately, after considerable search, I could not find such a course.  (There are some older brief tutorials that do not take advantage of the features in the new Physics package.)  I am sure that there must be some physics courses that are based around this Physics Package, certainly at the University of Waterloo or the Perimeter Institute.  I would like to suggest that these courses be made available online (with a fee if necessary).  If such courses were available I know that I would avidly use them as I am sure would many others.

## Feynman Diagram by Physics Package?...

Is there currently any way to perform Feynman integration after applying the Feynman rules for various electrodynamics processes?

Can maple 2016 do renormalization of integrals? If we cannot currently do any of these, when will this features be available? Thank You very much.

## Certain issues in Physics...

I thought I'd try the latest version of the physics package. I am trying to look at a "simple" function with quantum operators, Taylor expand it, and write terms in normal order (i.e. Dagger(a) terms before a, and Dagger(b) before b), but am having no luck at all. Not sure if this is possible with the current version.

I am also having a couple of weird "interface issues" after loading the package:
1) See the printout from Setup() command - here Dagger(a) and Dagger(b) is sometimes displayed with a bar above the names, but other times (i.e. during other runs) with daggers.
2) Maple gets "stuck" on one of the lines - meaning I press enter, but it does not jump to the next execution block.

Both of these issues are outlined with "NOTE" in the worksheet.

Ultimately, the interface issues are of no concern to me, but I am pretty curious if the current version of the physics package can do what I need?

thanks

Worksheet:  commutator_stuff.mw

---------------------------------

## Trace in Physics package at Maple14...

I try to repeat lines (25)-(28) at

http://www.maplesoft.com/support/help/maple/view.aspx?path=Physics%2fTrace#commentform

I use Maple 14. However, instead of (28) I get the following result:

It means that Maple 14 does not perceive p_\mu, k_\nu and m as scalar quantities. I would like to ask how to define these variables correctly.