Why the space is isotropic in the vector particle's decay?

[Ganesh Ujwal]

I come cross one proof the Landau-Yang Theorem, which states that a [latex]J^P=1^+[/latex] particle cannot decay into two photons, in this paper (page 4).

The basic idea is, the photon's wavefunction should be symmetric under exchange, however the spin part is anti-symmetric and the space part is symmetric and therefore forbidden.

I have trouble understanding the argument about the space part:

Since the photons conserve linear momentum in the particle rest frame and space is isotropic, they must be emitted in spherical waves.

Why the space is isotropic? Is isotropy an intrinsic property of original particle or just because the final particles are identical?

I guess the right answer is the latter one, because [latex]\rho^+ \to \pi^+ \pi^0[/latex] the final pions lie in [latex]P[/latex] wave and it doesn't bothered by the Bose-Einstein statistics. (Compare this with [latex]\rho^0\to \pi^0 \pi^0[/latex], which is forbidden.)

However, I still believe the isotropy is an intrinsic property of the original particle. I'm looking for an explanation more mathematically, or a definition of isotropy in the language of group theory.

Any suggestions?

[ALex7JA]

Okay. Well the fundamental theorem states, in theory in absolute Lehman's terms that where there is something, there cannot be something else.

 

A bit more information exchange would say that a mirror in space, something is already there, cannot go through the mirror, so the only photons that can be are around that mirror not inside it, because something is already there

 

Mathematical Equation showing space wavefunction

 

Let A(1) be the photon, B(2) the space, c(3) time, D(4) the wavefunction exact phenomenon

 

A + B = C (In this example c functions everyday juxtaposing)

 

In the event that the photon is parallel matched, wavefunction exact, then, if forceful science is used (which I don't recommend at all) CII denotes the critically unstable energy

 

A+ D = CII ( in this example CII functions flame alignments whereby the blue flame is inside yet the white flame is outside, then the blue flame burns up and becomes white)

Edited January 14, 2015 by ALex7JA