Undergrad Coupling Spin-0 and spin-1 fields

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SUMMARY

The discussion centers on the formulation of a wave function for a combined spin-1 and spin-0 field, specifically addressing the concept of direct product states versus linear superpositions. Participants clarify that a linear superposition of these spins does not exist, emphasizing the need for a direct product state representation. The proposed wave function is expressed as ##\Psi^{\mu}(x,y)=\phi(x) \psi^{\mu}(y)##, indicating a multi-particle wave function approach to combine these fields.

PREREQUISITES
  • Understanding of quantum field theory concepts
  • Familiarity with spin-0 and spin-1 particle properties
  • Knowledge of wave function formulation in quantum mechanics
  • Experience with direct product states in quantum systems
NEXT STEPS
  • Research the mathematical formulation of direct product states in quantum mechanics
  • Explore the implications of multi-particle wave functions in quantum field theory
  • Study the properties and behaviors of spin-0 and spin-1 particles
  • Investigate the limitations of linear superpositions in quantum systems
USEFUL FOR

Physicists, quantum field theorists, and students studying particle physics who are interested in the interactions and representations of combined spin 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)##
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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