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Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something more rich/subtle than just saying the Hilbert Space are composed by the state space of infinite many sets and infinite many modes of harmonic oscillators? - i.e. more rich/subtle than usual spin-0 scalar fields' Hilbert space?) Is the quantum Gauge theory's Hilbert Space written in a tensor product form or not (eg. thinking about put this gauge theory on the lattice)?

Whether there are differences for this procedure construction of Hilbert space for these three cases:

(1) spin-1 quantum Gauge theory with Abelian $U(1)$ symmetry

(2) spin-1 quantum Gauge theory with non-Abelian (such as $SU(N)$) symmetry

(3) spin-2 quantum Gauge theory (Gravity? or anything else)

Also, whether gauge-redundancy plays any roles? Is there similar thing like Fadeev-Popov ghosts happened in the path integral formalism, when one dealing with gauge-redundancy?

Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something more rich/subtle than just saying the Hilbert Space are composed by the state space of infinite many sets and infinite many modes of harmonic oscillators? - i.e. more rich/subtle than usual spin-0 scalar fields' Hilbert space?) Is the quantum Gauge theory's Hilbert Space written in a tensor product form or not (eg. thinking about put this gauge theory on the lattice)?

Whether there are differences for this procedure construction of Hilbert space for these three cases:

(1) spin-1 quantum Gauge theory with Abelian $U(1)$ symmetry

(2) spin-1 quantum Gauge theory with non-Abelian (such as $SU(N)$) symmetry

(3) spin-2 quantum Gauge theory (Gravity? or anything else)

Also, whether gauge-redundancy plays any roles? Is there similar thing like Faddeev-Popov ghosts happened in the path integral formalism, when one dealing with gauge-redundancy?

Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something more rich/subtle than just saying the Hilbert Space are composed by the state space of infinite many sets and infinite many modes of harmonic oscillators? - i.e. more rich/subtle than usual spin-0 scalar fields' Hilbert space?) Is the quantum Gauge theory's Hilbert Space written in a tensor product form or not (eg. thinking about put this gauge theory on the lattice)?

Whether there are differences for this procedure construction of Hilbert space for these three cases:

(1) spin-1 quantum Gauge theory with Abelian U(1) symmetry

(2) spin-1 quantum Gauge theory with non-Abelian (such as SU(N)) symmetry

(3) spin-2 quantum Gauge theory (Gravity? or anything else)

also whether gauge-redundancy plays any roles? Is there similar thing like Fadeev-Popov ghosts happened in the path integral formalism, when one dealing with gauge-redundancy?

Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something more rich/subtle than just saying the Hilbert Space are composed by the state space of infinite many sets and infinite many modes of harmonic oscillators? - i.e. more rich/subtle than usual spin-0 scalar fields' Hilbert space?) Is the quantum Gauge theory's Hilbert Space written in a tensor product form or not (eg. thinking about put this gauge theory on the lattice)?

Whether there are differences for this procedure construction of Hilbert space for these three cases:

(1) spin-1 quantum Gauge theory with Abelian $U(1)$ symmetry

(2) spin-1 quantum Gauge theory with non-Abelian (such as $SU(N)$) symmetry

(3) spin-2 quantum Gauge theory (Gravity? or anything else)

Also, whether gauge-redundancy plays any roles? Is there similar thing like Fadeev-Popov ghosts happened in the path integral formalism, when one dealing with gauge-redundancy?

Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something more rich/subtle than just saying the Hilbert Space are composed by the state space of infinite many sets and infinite many modes of harmonic oscillators? - i.e. more rich/subtle than usual spin-0 scalar fields' Hilbert space?)

Whether there are differences for this procedure construction of Hilbert space for these three cases:

(1) spin-1 quantum Gauge theory with Abelian U(1) symmetry

(2) spin-1 quantum Gauge theory with non-Abelian (such as SU(N)) symmetry

(3) spin-2 quantum Gauge theory (Gravity? or anything else)

also whether gauge-redundancy plays any roles? Is there similar thing like Fadeev-Popov ghosts happened in the path integral formalism, when one dealing with gauge-redundancy?

Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something more rich/subtle than just saying the Hilbert Space are composed by the state space of infinite many sets and infinite many modes of harmonic oscillators? - i.e. more rich/subtle than usual spin-0 scalar fields' Hilbert space?) Is the quantum Gauge theory's Hilbert Space written in a tensor product form or not (eg. thinking about put this gauge theory on the lattice)?

Whether there are differences for this procedure construction of Hilbert space for these three cases:

(1) spin-1 quantum Gauge theory with Abelian U(1) symmetry

(2) spin-1 quantum Gauge theory with non-Abelian (such as SU(N)) symmetry

(3) spin-2 quantum Gauge theory (Gravity? or anything else)

also whether gauge-redundancy plays any roles? Is there similar thing like Fadeev-Popov ghosts happened in the path integral formalism, when one dealing with gauge-redundancy?