Coupling Spin-0 and spin-1 fields

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Discussion Overview

The discussion revolves around the formulation of a wave function for a system that combines spin-1 and spin-0 fields. Participants explore the nature of such combinations, particularly focusing on whether they can be represented as direct product states or linear superpositions.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how to obtain a wave function for a combined spin-1 and spin-0 field, noting a lack of resources on this topic.
  • Another participant seeks clarification on whether the term "combined" refers to a direct product state or a linear superposition, asserting that the latter does not exist.
  • A subsequent reply reiterates the need for clarification on the nature of the combination, suggesting that if the fields were treated as a single object, a multi-particle wave function could be considered.
  • One participant proposes a specific form for the direct product state, indicating it might take the form of ##\Psi^{\mu}(x,y)=\phi(x) \psi^{\mu}(y)##.

Areas of Agreement / Disagreement

Participants express differing views on the nature of combining spin-1 and spin-0 fields, with some uncertainty about the validity of linear superpositions in this context. The discussion does not reach a consensus on the appropriate formulation.

Contextual Notes

Participants do not fully resolve the assumptions regarding the definitions of "combined" states and the implications of treating the fields as a single object. There are also unresolved questions about the mathematical representation of these states.

PLANCKTHEORY
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My question is, how does one get a wave function for a 'combined' spin-1 and a spin-0 field? How is this possible? I have only been able to find combined states for equal spin identical particles.

If you don't understand my question, I'll be glad to reword it.
 
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What do you mean "combined spin 1 and spin 0"? A direct product state, or a linear superposition? The latter doesn't exist.
 
dextercioby said:
What do you mean "combined spin 1 and spin 0"? A direct product state, or a linear superposition? The latter doesn't exist.
Basically, if they were one object. I suppose like a multi particle wave function. What would the Direct product state be like?
 
PLANCKTHEORY said:
Basically, if they were one object. I suppose like a multi particle wave function. What would the Direct product state be like?
It would be something like
##\Psi^{\mu}(x,y)=\phi(x) \psi^{\mu}(y)##
 

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