and their physical/mathematical meanings.

          Alg( Hilb )         Algebra of bounded operators on Hilb
          Alg( Hilb(n) )      Algebra of bounded operators on Hilb(n)
          Alg(n)              = Alg( Hilb(n) )
          B                   QM annihilation operator
          B!                  QM creation operator
          B(n)                Truncated annihilation operator
          B!(n)               Truncated creation operator
         ~B(n)                Skew truncated annihilation operator
         ~B!(n)               Skew truncated creation operator
          C(n) C!(n)          Cyclic matrices
          C                   The complex field
          CHAH_k(z)           k-th Chebyshev polynomial od the first kind
          D_k(z)              Parabolic Cylinder functions
         ~D_k(z)              Normalized Parabolic Cylinder functions
          d_k                 Column normalizing factor of XI(n)
          delta_kj            Kronecker delta
          delta_(kj)          Kronecker delta
          epsilon_ijk         Permutation symbol (Epsilon density)
          epsilon_(ijk)       Permutation symbol (Epsilon density)
          F(n)                Generator for C(n)
          Fr(n)               Q-P finite Fourier transform
          G(n)                Fundamental Indefinite form on Hilb(n)
          Hilb                A separable infinite dimensional Hilbert space
          Hilb(n)             An n-dimensional Hilbert space
          Hilb_+(n)           G(n)-positive part of Hilb(n)
          Hilb_-(n)           G(n)-negative part of Hilb(n)
          Hilb_0(n)           G(n)-null part of Hilb(n)
          H(n)                Radial operator in pseudo-polar form for
                              B(n) and B!(n)
          H_k(z)              Unnormalized k-th Hermite polynomial
         ~H_k(z)              Normalized k-th Hermite polynomial
          h-bar               Reduced Plank constant
          I                   Identity in Alg(Hilb)
          I(n)                nXn identity
          L                   A Lie algebra
          L*                  A complexified Lie algebra
          lambda_k(n)         The (3) dimensional IRREP of su(3)
          N                   QM Number operator
          N(n)                Truncated Number operator
          N'(n)               Truncated Number operator
          N_-(n)              Truncated Number operator with negative
          P                   QM Momentum operator
          P(n)                Truncated "Momentum" operator
          P'(n)               Truncated "Momentum" operator
          PHI                 Abstract Fourier transform
          PI(n)               Diagonalizer of P(n)
          Q                   QM Position operator
          Q(n)                Truncated "Position" operator
          Q'(n)               Truncated "Position" operator
          rho( A )            Spectral radius of operator A
          S_a(n)              Generators for n dimensional IRREP of su(2)
          Sp( A )             Spectrum of operator A
          sigma_k             Normalized Pauli spin matrices
          SHA                 Shift operator on a one-side infinitely
          SHA(n) SHA!(n)      Nilpotent shift operators on Hilb(n)
          t(n), t_(+|-)(n)    Time operators
          Tr( A )             Trace of operator A
          U_g(n)              Kinematical invariance group of
                                   canonical transformations
          U(G, n)             Kinematical invariance group of
                                   canonical transformations
          UPSILON(n)          N-F-M finite Fourier transform
                                   and diagonalizer of C(n)
          X_a(n)              2 dimensional IRREP of su(2)
          XI(n)               Diagonalizer of Q(n)
          Y_a(n)              Canonical bilinears
          Z                   Dense invariant domain in Hilb for B and B!

          |n, k>              Eigenvectors of N(n)
          |q(n, k)>           Eigenvectors of Q(n)
          |p(n, k)>           Eigenvectors of P(n)
          |mu(n, k)>          Eigenvectors of C(n)

          !                   Complex conjugate transpose
          *                   Complex conjugate

          CM             Classical Mechanics
          CCR            Canonical Commutation Relation
          CAR            Canonical Anticommutation Relation
          EM             Classical Electromagnetic theory
          FCCR           Finite Canonical Commutation Relation
          GR             General Relativity
          IRREP          Irreducible Representation
          LGH            Left G(n)-Hermitean
          LGS            Left G(n)-skew Hermitean
          QFT            Quantum Field Theory
          QG             Quantum Gravity
          QST            Quantum Space-Time
          QM             Standard Quantum Mechanics
          RGH            Right G(n)-Hermitean
          RGS            Right G(n)-skew Hermitean
          RQM            Relativistic Quantum Mechanics
          SR             Special Relativity
          UIRREP         Unitary Irreducible Representation

FCCR Table of Contents

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