User Filippo

41 votes

3 answers

3k views

Do all Noether theorems have a common mathematical structure?

asked Dec 2, 2020 at 14:18

10 votes

3 answers

1k views

Why is absolute time considered an axiom of Newtonian mechanics? What statements are based on this axiom?

asked Jun 25, 2021 at 8:44

9 votes

1 answer

582 views

Spectral decomposition vs Taylor Expansion

asked Nov 30, 2020 at 12:06

8 votes

1 answer

904 views

Two different versions of Schrödinger's equation - are they equivalent?

asked Nov 7, 2020 at 17:15

8 votes

3 answers

547 views

Is the Born rule usually regarded an axiom in quantum mechanics?

asked Sep 11, 2021 at 9:46

6 votes

2 answers

128 views

$A^{\alpha}=(\phi,\vec{A})$ or $A_{\alpha}=(\phi,\vec{A})$?

asked Nov 1, 2020 at 21:26

6 votes

5 answers

657 views

How are vector quantities in three dimensions (velocity, electric field, etc.) modeled in mathematical physics?

asked Dec 4, 2020 at 15:33

4 votes

2 answers

576 views

Dirac-delta-functions as eigenbasis of the position operator - pure nonsense? Or can more be said?

asked Jan 11, 2021 at 11:06

4 votes

1 answer

183 views

A critical step in Fujikawa's proof of the Atiyah Singer index theorem

asked Apr 26, 2021 at 7:04

3 votes

1 answer

133 views

When and why can the spin connection term of the Dirac Operator be omitted?

asked Apr 6, 2021 at 16:36

3 votes

2 answers

390 views

Definition of $k^0$ in Getzler's proof of the Atiyah-Singer index theorem

asked May 3, 2021 at 10:53

3 votes

1 answer

404 views

Proof that conservation of momentum is Lorentz invariant

asked Aug 10, 2022 at 18:44

3 votes

1 answer

105 views

The inhomogeneous Maxwell equation ${}\mathrm d{}F=J^\flat$ is only true for the signature $(+---)$?

asked Nov 21, 2022 at 15:01

3 votes

2 answers

159 views

Reference request - derivation of $\mathrm{ind}\,D_+=-\frac{1}{8\pi^2}\int\text{tr}\,F\wedge F$

asked Mar 13, 2021 at 18:39

3 votes

3 answers

171 views

What is the equivalent to $\Box A^\alpha =- \mu_0 J^\alpha$ using differential forms?

asked Nov 3, 2020 at 11:29

3 votes

0 answers

180 views

HaMiDeW coefficients - recursive calculation of the coincidence limits

asked Mar 16 at 16:02

2 votes

3 answers

154 views

Calling angles dimensionless and simultaneously distinguishing between numbers and angles is inconsistent, isn't it?

asked Jul 30, 2022 at 21:00

2 votes

0 answers

62 views

Ising model - Two different Gibbs distributions? (Friedli-Velenik)

asked Jun 28 at 13:58

2 votes

1 answer

58 views

Differential operators in QM whose domain is a subspace of $L^2$ act on equivalence classes - How is that even defined?

asked Nov 7, 2020 at 20:54

2 votes

3 answers

237 views

Is the equation $[\nabla_{\mu},\nabla_{\nu}]=F_{\mu\nu}$ correct? If yes, how does it have to be interpreted?

asked Mar 19, 2021 at 16:34

2 votes

2 answers

402 views

Gauge theory - definition of the trace

asked Mar 24, 2021 at 14:19

2 votes

3 answers

207 views

Explanation of $\sum_n\langle\psi_n(x)|(O\psi_n)(x)\rangle=:(\mathrm{tr}\,O)(x)=\mathrm{tr}\int\frac{\mathrm{d}k}{(2\pi)^4}e^{ikx}Oe^{-ikx}$

asked Mar 29, 2021 at 8:53

2 votes

1 answer

72 views

I get an extra term when I try to derive $\nabla\!\!\!\!/\ ^2=\nabla_\mu \nabla^\mu+\frac{1}{4}[\gamma^\mu,\gamma^\nu]F_{\mu\nu}$

asked Mar 31, 2021 at 13:14

2 votes

1 answer

80 views

The Lorentz group is only equal to $O(1,3)$ if $c=1$?

asked Sep 13, 2022 at 19:07

2 votes

1 answer

147 views

A formulation of (classical) electrodynamics using fiber bundles

asked Jun 22, 2021 at 13:26

2 votes

1 answer

113 views

Exponential of operators not defined on a Hilbert space (Dirac operator)

asked Apr 9, 2021 at 11:59

1 vote

1 answer

69 views

Is $k_t(x,x)\sim(4\pi t)^{-n/2}\mathrm{e}^{-tF}$ if $R=0$? (Dirac operator, heat kernels)

asked Apr 29, 2021 at 8:04

1 vote

0 answers

122 views

Given the mass density $\rho(x):=1/|x|$, a ball centered in the origin contains a finite amount of mass

asked Nov 1, 2021 at 15:06

1 vote

2 answers

155 views

On the proof that $4$-velocity transforms like vector

asked Sep 14, 2022 at 13:20

1 vote

1 answer

141 views

Interpretation of Lorentz boosts

asked Aug 19, 2022 at 20:00

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45 Questions

Do all Noether theorems have a common mathematical structure?

Why is absolute time considered an axiom of Newtonian mechanics? What statements are based on this axiom?

Spectral decomposition vs Taylor Expansion

Two different versions of Schrödinger's equation - are they equivalent?

Is the Born rule usually regarded an axiom in quantum mechanics?

$A^{\alpha}=(\phi,\vec{A})$ or $A_{\alpha}=(\phi,\vec{A})$?

How are vector quantities in three dimensions (velocity, electric field, etc.) modeled in mathematical physics?

Dirac-delta-functions as eigenbasis of the position operator - pure nonsense? Or can more be said?

A critical step in Fujikawa's proof of the Atiyah Singer index theorem

When and why can the spin connection term of the Dirac Operator be omitted?

Definition of $k^0$ in Getzler's proof of the Atiyah-Singer index theorem

Proof that conservation of momentum is Lorentz invariant

The inhomogeneous Maxwell equation ${}\mathrm d{}F=J^\flat$ is only true for the signature $(+---)$?

Reference request - derivation of $\mathrm{ind}\,D_+=-\frac{1}{8\pi^2}\int\text{tr}\,F\wedge F$

What is the equivalent to $\Box A^\alpha =- \mu_0 J^\alpha$ using differential forms?

HaMiDeW coefficients - recursive calculation of the coincidence limits

Calling angles dimensionless and simultaneously distinguishing between numbers and angles is inconsistent, isn't it?

Ising model - Two different Gibbs distributions? (Friedli-Velenik)

Differential operators in QM whose domain is a subspace of $L^2$ act on equivalence classes - How is that even defined?

Is the equation $[\nabla_{\mu},\nabla_{\nu}]=F_{\mu\nu}$ correct? If yes, how does it have to be interpreted?

Gauge theory - definition of the trace

Explanation of $\sum_n\langle\psi_n(x)|(O\psi_n)(x)\rangle=:(\mathrm{tr}\,O)(x)=\mathrm{tr}\int\frac{\mathrm{d}k}{(2\pi)^4}e^{ikx}Oe^{-ikx}$

I get an extra term when I try to derive $\nabla\!\!\!\!/\ ^2=\nabla_\mu \nabla^\mu+\frac{1}{4}[\gamma^\mu,\gamma^\nu]F_{\mu\nu}$

The Lorentz group is only equal to $O(1,3)$ if $c=1$?

A formulation of (classical) electrodynamics using fiber bundles

Exponential of operators not defined on a Hilbert space (Dirac operator)

Is $k_t(x,x)\sim(4\pi t)^{-n/2}\mathrm{e}^{-tF}$ if $R=0$? (Dirac operator, heat kernels)

Given the mass density $\rho(x):=1/|x|$, a ball centered in the origin contains a finite amount of mass

On the proof that $4$-velocity transforms like vector

Interpretation of Lorentz boosts