Fractional Gravity/Cosmology in Classical and Quantum Regimes
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".
Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 7436
Special Issue Editors
Interests: general relativity; quantum field theory; gravitational physics; quantum mechanics; theoretical particle; physics; high energy physics
Special Issues, Collections and Topics in MDPI journals
Interests: theoretical physics, quantum gravity, quantum cosmology, foundations of quantum mechanics
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
In fractional calculus, the power of the differentiation operator (which is not local) is any rational (or even real or complex) number. Recently, this has been widely used in various branches of physics. Such frameworks have played an important role in understanding complex systems in both the classical and quantum regimes. In what follows, we will focus on fractional gravity and cosmology.
Regarding the classical regime, the fractional derivative cosmology has been established by two different methods: (i) The last-step modification method is the simplest one, in which the given cosmological field equations for a specific model are replaced by the corresponding fractional field equations. (ii) The first-step modification method can be considered a more fundamental methodology. In this method one, starts by establishing fractional derivative geometry. More concretely, the variational principle for the fractional action is applied to establish a modified cosmological model.
The main objective of the mentioned methods is the investigation of open problems in gravity/cosmology.
In the context of fractional quantum mechanics, the fractional Schrödinger equation (SE) has been obtained with space, time and space–time fractional derivatives. These frameworks have been applied to solve various problems with different potentials. Moreover, fractional quantum mechanics has been applied as a tool within quantum field theory and gravity for fractional spacetime. Inspired by the modified SE mentioned above, the fractional Wheeler–DeWitt equation associated with the fractional quantum cosmology was also set up.
New ideas, current developments, future perspectives and review articles on the above fractional proposals relevant to gravitation and cosmology are the focus of this Issue and are welcome.
Dr. Seyed Meraj Mousavi Rasouli
Dr. Shahram Jalalzadeh
Guest Editors
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Keywords
- fractional calculus
- fractional derivatives
- Riesz fractional operator
- Caputo fractional operator
- fractional Brownian motion
- Lévy path integrals
- fractional action-like variational approach
- fractional quantum mechanics
- fractional classical cosmology
- fractional quantum cosmology
- non-local operators
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