scholarly journals POISSON BRACKET IN CLASSICAL FIELD THEORY AS A DERIVED BRACKET

2008 ◽  
Vol 05 (07) ◽  
pp. 1051-1055
Author(s):  
S. A. POL'SHIN
Keyword(s):  
Field Theory ◽  
Poisson Bracket ◽  
Maxwell Equations ◽  
Differential Forms ◽  
Classical Field Theory ◽  
Classical Field ◽  
Hamiltonian Form ◽  
Jet Bundle ◽  
Finite Dimensional ◽  
Derived Bracket

We construct a Leibniz bracket on the space Ω• (Jk (π)) of all differential forms over the finite-dimensional jet bundle Jk (π). As an example, we write Maxwell equations with sources in the covariant finite-dimensional hamiltonian form.

scholarly journals Asymptotic Conservation Laws in Classical Field Theory

1996 ◽  
Vol 77 (20) ◽  
pp. 4109-4113 ◽  
Author(s):  
Ian M. Anderson ◽  
Charles G. Torre
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Classical Field Theory ◽  
Classical Field

Emerson's Atom and the Matter of Suffering

2009 ◽  
Vol 64 (1) ◽  
pp. 16-47
Author(s):  
Mark Noble
Keyword(s):  
Field Theory ◽  
Natural History ◽  
Classical Field Theory ◽  
Classical Field ◽  
The Other ◽  
History Of ◽  
The One ◽  
The Individual ◽  
Solid Bodies ◽  
Lines Of Force

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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