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In this book, the author presents the theory of quasifree quantum
fields and argues that they could provide non-zero scattering for
some particles. The free-field representation of the quantised
transverse electromagnetic field is not closed in the
weak*-topology. Its closure contains soliton-anti-soliton pairs as
limits of two-photon states as time goes to infinity, and the
overlap probability can be computed using Uhlmann's prescription.
There are no free parameters: the probability is determined with no
requirement to specify any coupling constant. All cases of the
Shale transforms of the free field of the form + , where is not in
the one-particle space, are treated in the book. There remain the
cases of the Shale transforms of the form T , where T is a
symplectic map on the one-particle space, not near the identity.
How can one construct dynamical systems obeying the first and
second laws of thermodynamics: mean energy is conserved and entropy
increases with time? This book answers the question for classical
probability (Part I) and quantum probability (Part II). A novel
feature is the introduction of heat particles which supply thermal
noise and represent the kinetic energy of the molecules. When
applied to chemical reactions, the theory leads to the usual
nonlinear reaction-diffusion equations as well as modifications of
them. These can exhibit oscillations, or can converge to
equilibrium. In this second edition, the text is simplified in
parts and the bibliography has been expanded. The main difference
is the addition of two new chapters; in the first, classical fluid
dynamics is introduced. A lattice model is developed, which in the
continuum limit gives us the Euler equations. The five
Navier???Stokes equations are also presented, modified by a
diffusion term in the continuity equation. The second addition is
in the last chapter, which now includes estimation theory, both
classical and quantum, using information geometry.
How can one construct dynamical systems obeying the first and
second laws of thermodynamics: mean energy is conserved and entropy
increases with time? This book answers the question for classical
probability (Part I) and quantum probability (Part II). A novel
feature is the introduction of heat particles which supply thermal
noise and represent the kinetic energy of the molecules. When
applied to chemical reactions, the theory leads to the usual
nonlinear reaction-diffusion equations as well as modifications of
them. These can exhibit oscillations, or can converge to
equilibrium. In this second edition, the text is simplified in
parts and the bibliography has been expanded. The main difference
is the addition of two new chapters; in the first, classical fluid
dynamics is introduced. A lattice model is developed, which in the
continuum limit gives us the Euler equations. The five
Navier???Stokes equations are also presented, modified by a
diffusion term in the continuity equation. The second addition is
in the last chapter, which now includes estimation theory, both
classical and quantum, using information geometry.
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