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Symmetry Breaking in Projective Gaug...

Connolly, Michael J.,

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Symmetry Breaking in Projective Gauge Gravity /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Symmetry Breaking in Projective Gauge Gravity // Michael J Connolly.
作者:	Connolly, Michael J.,
面頁冊數:	1 electronic resource (107 pages)
附註:	Source: Masters Abstracts International, Volume: 86-01.
Contained By:	Masters Abstracts International86-01.
標題:	Theoretical physics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31239199
ISBN:	9798383190692

Symmetry Breaking in Projective Gauge Gravity /
Connolly, Michael J.,

Symmetry Breaking in Projective Gauge Gravity /Michael J Connolly. - 1 electronic resource (107 pages)

Source: Masters Abstracts International, Volume: 86-01.

The Thomas-Whitehead (TW) projective theory of gravity has its origin in 1 + 1(+1) dimensional string theory. The coadjoint elements of the Virasoro algebra contain the Diffeomorphism field, identified by its transformation behavior under the coadjoint action. Through a correspondence with Sturm-Liouville operators, the Diffeomorphism field is identified with the potential. When lifted to a higher dimensional classical theory, the Diffeomorphism field appears as a component of a projective connection.In m spacetime dimensions, the projective spin connection, rather, the framed projective connection appears as a nonlinear connection taking values in the Lie algebra of a particular subgroup of the general linear group in m + 1 dimensions. These vertical translations are restored and a composite coset element is formed. The resulting nonlinear connection may be viewed as a general pre-projective connection. Emphasis is put on the utilization of covariant generalized Higgs fields in this construction. Some properties of the present connection are investigated and compared with what is known about the TW projective connection.This document seeks a basis-independent description of projective gravity, wherein the recently discovered Diffeomorphism field retains dynamics. Without an additional metric structure, only one option presents itself as a governing action functional. The projective Pontryagin density is formed and the associated Chern-Simons forms computed. The latter appear nearly identical to the Chern-Simons forms of Metric-Affine gravitational gauge theories coupled to a scalar field when expanded about the maximally symmetric (anti) de Sitter solutions. In a similar fashion, the associated field equations serve to produce the Bianchi identities.Once a metric structure is introduced, further action functionals become available. However, this imposition requires the stability group be Lorentzian. This makes available a notion of Lie algebra dual. Two dual operations are considered. The first follows the work of Stelle and West, utilizing a fundamental algebraic vector field to explicitly reduce the symmetry group. The second is an ordinary duality, which is utilized to form a Lovelock-type action. Both models are solved and discussed. None of these models appear to produce dynamics for the Diffeomorphism field.Matter fields are here considered in the nonlinear setting. This straight-forward process reveals a discrepancy when compared to the common uses of projective matter fields. In avoidance of this, the common form is adopted and all new structure reduced, such that the setting which results is that of TW theory. The TW-Dirac model is revisited and written in a manifestly covariant form upon the dimensional reduction to spacetime. A non-hermitian chiral coupling to the Diffeomorphism scalar is re-confirmed. However, the induced chiral mass is shown to contain both hermiticity-respecting and violating contributions. The implications of this are left for future work.

English

ISBN: 9798383190692Subjects--Topical Terms:

2144760
Theoretical physics.
Subjects--Index Terms:

Diffeomorphism field

Symmetry Breaking in Projective Gauge Gravity /
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500 $a Advisors: Rodgers, Vincent G. J. Committee members: Stiffler, Kory; Polyzou, Wayne; Jorgensen, Palle.
502 $b M.S. $c The University of Iowa $d 2024.
520 $a The Thomas-Whitehead (TW) projective theory of gravity has its origin in 1 + 1(+1) dimensional string theory. The coadjoint elements of the Virasoro algebra contain the Diffeomorphism field, identified by its transformation behavior under the coadjoint action. Through a correspondence with Sturm-Liouville operators, the Diffeomorphism field is identified with the potential. When lifted to a higher dimensional classical theory, the Diffeomorphism field appears as a component of a projective connection.In m spacetime dimensions, the projective spin connection, rather, the framed projective connection appears as a nonlinear connection taking values in the Lie algebra of a particular subgroup of the general linear group in m + 1 dimensions. These vertical translations are restored and a composite coset element is formed. The resulting nonlinear connection may be viewed as a general pre-projective connection. Emphasis is put on the utilization of covariant generalized Higgs fields in this construction. Some properties of the present connection are investigated and compared with what is known about the TW projective connection.This document seeks a basis-independent description of projective gravity, wherein the recently discovered Diffeomorphism field retains dynamics. Without an additional metric structure, only one option presents itself as a governing action functional. The projective Pontryagin density is formed and the associated Chern-Simons forms computed. The latter appear nearly identical to the Chern-Simons forms of Metric-Affine gravitational gauge theories coupled to a scalar field when expanded about the maximally symmetric (anti) de Sitter solutions. In a similar fashion, the associated field equations serve to produce the Bianchi identities.Once a metric structure is introduced, further action functionals become available. However, this imposition requires the stability group be Lorentzian. This makes available a notion of Lie algebra dual. Two dual operations are considered. The first follows the work of Stelle and West, utilizing a fundamental algebraic vector field to explicitly reduce the symmetry group. The second is an ordinary duality, which is utilized to form a Lovelock-type action. Both models are solved and discussed. None of these models appear to produce dynamics for the Diffeomorphism field.Matter fields are here considered in the nonlinear setting. This straight-forward process reveals a discrepancy when compared to the common uses of projective matter fields. In avoidance of this, the common form is adopted and all new structure reduced, such that the setting which results is that of TW theory. The TW-Dirac model is revisited and written in a manifestly covariant form upon the dimensional reduction to spacetime. A non-hermitian chiral coupling to the Diffeomorphism scalar is re-confirmed. However, the induced chiral mass is shown to contain both hermiticity-respecting and violating contributions. The implications of this are left for future work.
546 $a English
590 $a School code: 0096
650 4 $a Theoretical physics. $3 2144760
650 4 $a Applied physics. $3 3343996
650 4 $a Physics. $3 516296
653 $a Diffeomorphism field
653 $a Higgs fields
653 $a Chern-Simons forms
653 $a Lovelock-type action
690 $a 0753
690 $a 0215
690 $a 0605
710 2 $a The University of Iowa. $b Physics. $e degree granting institution. $3 3816149
720 1 $a Rodgers, Vincent G. J. $e degree supervisor.
773 0 $t Masters Abstracts International $g 86-01.
790 $a 0096
791 $a M.S.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31239199