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The relation between substitutional symmetry operations that leave a real symmetric matrix invariant and the degeneracies exhibited by the matrix in diagonal form are examined. The usual application of group theory to this problem is formulated. Substitutional (and other) symmetries can exist,...
The canonical resolution of the multiplicity problem for tensor operators in SU(3) is equivalent to the map (the denominator mapping) from the set of all SU(3) unit tensor operators to SU(3) invariant functions (the denominator functions). The denominator function vanishes precisely on that...
The Virasoro algebra and group are examined in (3+1)‐dimensional theory with an Abelian gauge field coupled with the gravitational field. The two‐cocycle for the group is constructed by using the so‐called descent equation. Its infinitesimal version gives the Schwinger–Jackiw–Johnson...
Suppose that the state of a system of N n ‐level atoms is given by a tensor product of N identical density matrices. The exact formulas are presented that describe the probability that such a system may be found in a pure state with a given symmetry with respect to permutations of atoms. The...
Examples of grand canonical continuum models are given in R d , or a suitable subset of R d , for which no multiple phases exist.
In the context of the extension of the Hamilton–Jacobi theory to include Lagrangians involving higher derivatives the characteristic function seems not to have been considered. This omission is here rectified.
The finite‐temperature behavior of supersymmetry is considered from the viewpoint of stochastic field theory. To this end, it is considered that Nelson’s stochastic mechanics may be generalized to the quantization of a Fermi field when the classical analog of such a field is taken to be a...
The topology of the solutions derived in Part I J. Math. Phys. 2 8 , 1118 (1987) is discussed in detail using suitable topological embeddings. It is found that these solutions are homeomorphic to S 3 ×R, R 4 , or S 2 ×R 2 . Singularities and boundaries in these manifolds are examined within a...
Two‐cluster–two‐cluster scattering amplitudes are studied for N ‐body quantum systems with potentials that are both dilation analytic and exponentially decaying. It is proved that under quite broad assumptions these amplitudes can be meromorphically continued in the energy, with square...
For quantum field theories that do not satisfy the Wightman positivity condition, a Hilbert space structure condition is proposed, which guarantees a Krein structure for the space of states associated to the Wightman functions. The analogous problem for the Schwinger function is also discussed,...
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