2003/06/30 by Stephen L. Adler, L. P. Horwitz, Lawrence P. Horwitz
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Eigenvalues and eigenvectors #Invariant (physics) #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix function #Molecular spectroscopy and chirality #Partition function (quantum field theory) #Pascal matrix #Physics #Pure mathematics #Quantum mechanics #Symmetric matrix #TRACE (psycholinguistics) #Theoretical and Computational Physics #Unitary matrix #Unitary state #Vandermonde matrix #hep-th #quant-ph
paper · pdf · doi:10.1016/j.physletb.2003.07.025
published as Phys.Lett. B570 (2003) 73-81 · Tex, 22 pages
arxiv created 2003/07/28 · openalex publication_date 2003/08/12 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrix-valued correlation functions, that depend on the choice of unitary fixing. The unitary fixing is formulated within the standard Faddeev–Popov framework, in which the squared Vandermonde determinant emerges as a factor of the complete Faddeev–Popov determinant. We give the ghost representation for the FP determinant, and the corresponding BRST invariance of the unitary-fixed partition function. The formalism is relevant for deriving Ward identities obeyed by matrix-valued correlation functions.