Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time
The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger repre...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/11/1413 |
| _version_ | 1811298303968542720 |
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| author | Igor V. Kanatchikov |
| author_facet | Igor V. Kanatchikov |
| author_sort | Igor V. Kanatchikov |
| collection | DOAJ |
| description | The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended to arbitrary curved space-times. In the limiting case when the inverse of the ultraviolet parameter <inline-formula> <math display="inline"> <semantics> <mo>ϰ</mo> </semantics> </math> </inline-formula> introduced by precanonical quantization is mapped to the infinitesimal invariant spatial volume element, the canonical functional derivative Schrödinger equation is derived from the manifestly covariant partial derivative precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional spatial product integral of Clifford-algebra-valued precanonical wave function or the product integral of a scalar function obtained from the precanonical wave function by a sequence of transformations. In non-static space-times, the transformations include a nonlocal transformation given by the time-ordered exponential of the zero-th component of spin-connection. |
| first_indexed | 2024-04-13T06:17:28Z |
| format | Article |
| id | doaj.art-b640bf47e2144d5eab5559b36c500dd4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T06:17:28Z |
| publishDate | 2019-11-01 |
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| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b640bf47e2144d5eab5559b36c500dd42022-12-22T02:58:47ZengMDPI AGSymmetry2073-89942019-11-011111141310.3390/sym11111413sym11111413Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-TimeIgor V. Kanatchikov0School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UKThe functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended to arbitrary curved space-times. In the limiting case when the inverse of the ultraviolet parameter <inline-formula> <math display="inline"> <semantics> <mo>ϰ</mo> </semantics> </math> </inline-formula> introduced by precanonical quantization is mapped to the infinitesimal invariant spatial volume element, the canonical functional derivative Schrödinger equation is derived from the manifestly covariant partial derivative precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional spatial product integral of Clifford-algebra-valued precanonical wave function or the product integral of a scalar function obtained from the precanonical wave function by a sequence of transformations. In non-static space-times, the transformations include a nonlocal transformation given by the time-ordered exponential of the zero-th component of spin-connection.https://www.mdpi.com/2073-8994/11/11/1413quantum field theory in curved space-timede donder-weyl hamiltonian formalismprecanonical quantizationcanonical quantizationfunctional schrödinger representation |
| spellingShingle | Igor V. Kanatchikov Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time Symmetry quantum field theory in curved space-time de donder-weyl hamiltonian formalism precanonical quantization canonical quantization functional schrödinger representation |
| title | Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time |
| title_full | Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time |
| title_fullStr | Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time |
| title_full_unstemmed | Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time |
| title_short | Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time |
| title_sort | precanonical structure of the schrodinger wave functional of a quantum scalar field in curved space time |
| topic | quantum field theory in curved space-time de donder-weyl hamiltonian formalism precanonical quantization canonical quantization functional schrödinger representation |
| url | https://www.mdpi.com/2073-8994/11/11/1413 |
| work_keys_str_mv | AT igorvkanatchikov precanonicalstructureoftheschrodingerwavefunctionalofaquantumscalarfieldincurvedspacetime |