scholarly journals Canonical structure of classical field theory in the polymomentum phase space

1998 ◽  
Vol 41 (1) ◽  
pp. 49-90 ◽  
Author(s):  
Igor V. Kanatchikov
Author(s):  
Ion Vancea

In this paper, we are going to construct the classical field theory on the boundary of the embedding of \mathbb{R} \times S^{1}ℝ×S1 into the manifold MM by the Jacobi sigma model. By applying the poissonization procedure and by generalizing the known method for Poisson sigma models, we express the fields of the model as perturbative expansions in terms of the reduced phase space of the boundary. We calculate these fields up to the second order and illustrate the procedure for contact manifolds.


1999 ◽  
Vol 14 (07) ◽  
pp. 1087-1110 ◽  
Author(s):  
M. W. KALINOWSKI ◽  
W. PIECHOCKI

A symplectic structure of classical field theory and its application to the canonical geometric quantization procedure are presented. The developed formalism can be treated in two ways: as a prequantization procedure in the usual sense or as a quantization procedure in a stochastic quantum mechanics approach on a phase space.


1996 ◽  
Vol 77 (20) ◽  
pp. 4109-4113 ◽  
Author(s):  
Ian M. Anderson ◽  
Charles G. Torre

2009 ◽  
Vol 64 (1) ◽  
pp. 16-47
Author(s):  
Mark Noble

This essay argues that Ralph Waldo Emerson's interest in the cutting-edge science of his generation helps to shape his understanding of persons as fluid expressions of power rather than solid bodies. In his 1872 "Natural History of Intellect," Emerson correlates the constitution of the individual mind with the tenets of Michael Faraday's classical field theory. For Faraday, experimenting with electromagnetism reveals that the atom is a node or point on a network, and that all matter is really the arrangement of energetic lines of force. This atomic model offers Emerson a technology for envisioning a materialized subjectivity that both unravels personal identity and grants access to impersonal power. On the one hand, adopting Faraday's field theory resonates with many of the affirmative philosophical and ethical claims central to Emerson's early essays. On the other hand, however, distributing the properties of Faraday's atoms onto the properties of the person also entails moments in which materialized subjects encounter their own partiality, limitation, and suffering. I suggest that Emerson represents these aspects of experience in terms that are deliberately discrepant from his conception of universal power. He presumes that if every experience boils down to the same lines of force, then the particular can be trivialized with respect to the general. As a consequence, Emerson must insulate his philosophical assertions from contamination by our most poignant experiences of limitation. The essay concludes by distinguishing Emersonian "Necessity" from Friedrich Nietzsche's similar conception of amor fati, which routes the affirmation of fate directly through suffering.


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