Survey of Results,losely to one of these subjects or the other. It is the intent of this volume to introduce the reader to a more unified viewof symmetry groups in physics — both quantum and classical. The vehicle to achieve this approach is the study of quantum statistical physics of systems with high degree of symm
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Geometry of Polarizations, a complex distribution . such that .. The almost complex manifoldwill be denoted (M,j). And the smooth functions fin A(M) which satisfyXleft( f
ight) = 0 for all {V_F}left( M
ight) = left{ {X in {V^C}left( M
ight)|{X_m} in {F_m},m in M}
ight} is the algebraof holomorphic functions.
Fock Space,obtained by scalar extension. Let T = R/Z be the l-torus. The canonical homomorphism . is {mathop{
m e}
olimits} left( r
ight) = exp left( {2pi ir}
ight) for . in .. Assume . has an alternating bilinear form .. Then . for ., . in . is a 2-cocycle; so it defines a central extension Vof . by .. Vis
Borel-Weil Theory,s case. This development requires somewhat of a review of the classical theory of representations for Lie groups and algebras. One major result is the Borel–Weil theory for geometric realization of the representations. This is important, for as we show in the following chapters the geometric quantiz
Selberg Trace Theory, for quantum statistical physics of these spaces. ~ is noncompact, thus we will simplify the situation by studying . where r is a discrete subgroup of SL(2, R) chosen so that M is compact. This classical example was the original case studied by Maas,Selberg and others. More recently these and relate
Book 1983in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are
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Survey of Results,ics — both quantum and classical. The vehicle to achieve this approach is the study of quantum statistical physics of systems with high degree of symmetry — in particular the study of the high temperature asymptotics of these systems. These asymptotics provide the natural connection with classical (statistical) mechanics.
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