EMERGENCE OF THE LORENTZIAN STRUCTURE IN CLASSICAL FIELD THEORY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342018 ◽  
Author(s):  
SHINJI MUKOYAMA ◽  
JEAN-PHILIPPE UZAN
Keyword(s):  
Field Theory ◽  
Dimensional Space ◽  
Classical Field Theory ◽  
Effective Property ◽  
Positive Definite ◽  
Classical Field ◽  
Time Dimension ◽  
Flat Spacetime ◽  
Lorentzian Metric ◽  
Lorentzian Structure

The Lorentzian metric structure allows one to implement the relativistic notion of causality in any field theory and to define a notion of time dimension. We propose that at the microscopic level the metric is Riemannian and that the Lorentzian structure, usually thought as fundamental, is in fact an effective property, that emerges in some regions of a 4-dimensional space with a positive definite metric. We argue that a decent classical field theory for scalars, vectors and spinors in flat spacetime can be constructed, and that gravity can be included under the form of a covariant Galileon theory instead of general relativity.

First steps in classical field theory

2021 ◽  
pp. 435-448
Author(s):  
Andrew M. Steane
Keyword(s):  
Field Theory ◽  
Yukawa Potential ◽  
Classical Field Theory ◽  
Classical Field ◽  
Dirac Spinor ◽  
Dirac Equations ◽  
Flat Spacetime ◽  
Spinor Fields ◽  
The Relationship ◽  
Conserved Currents

Classical field theory, as it is applied to the most simple scalar, vector and spinor fields in flat spacetime, is described. The Klein-Gordan, Weyl and Dirac equations are obtained, and some features of their solutions are discussed. The Yukawa potential, the plane wave solutions, and the conserved currents are obtained. Spinors are introduced, both through physical pictures (flagpole and flag) and algebraic defintions (complex vectors). The relationship between spinors and four-vectors is given, and related to the Lie groups SU(2) and SO(3). The Dirac spinor is introduced.

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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