Quantum Field Theory
Overview
Interesting quantum spacetime phenomena, such as particle creation in a time-dependent gravitational field,illustrates how gravitation and quantum field theory interact. Amplification of quantum field fluctuations is an unavoidable consequence in a strongly time-dependent gravitational field. This amplification emphasizes the importance of the effect of the dynamics of spacetime on quantum fields. Physical implications of amplification are black hole evaporation (S. W. Hawking,1975.), acceleration radiation (W. G. Unruh 1976), accelerated boundary radiation (P. C. W. Davies and S. A. Fulling 1976,1977) cosmological particle creation (Leonard Parker 1969) and the inflationary model of the universe (Alan H. Guth 1981). My research has been motivated by the desire to understand the nonequilibrium radiation that occurs in the evolution of the particle production from the more general forms of strongly time-dependent accelerations. The starting point for this line of research lies in two key facts: 1. Thermal radiation from an accelerated observer, without late time approximation, requires a time-independent accelerated trajectory, i.e. uniform acceleration. (the Unruh Effect). 2. Thermal radiation from an accelerated boundary (the Davies-Fulling Effect), without late time approximation (Robert D. Carlitz and Raymond S. Willey 1987), requires a strongly time-dependent accelerated trajectory (Carlitz-Willey 1987). When a moving mirror is uniformly accelerated, it gives off non-thermal radiation (P. C. W. Davies and S. A. Fulling 1977). These two key facts, succinctly expressed are: • Uniform acceleration gives rise to the thermal Unruh effect. • Non-uniform acceleration gives rise to the thermal Davies-Fulling effect. (I have found this acceleration (Michael R.R. Good 2013) A key assumption of general relativity involves the complete physical equivalence of a gravitational field and a corresponding accelerated reference system. Since the effects of acceleration provide insight into the effects of gravitation, my goal is to appeal to acceleration phenomena which amplify quantum fluctuations. Quantum fluctuations driven by accelerations lies at the interface of quantum field theory and general relativity. Quantum field theory in curved spacetime has, since its inception in the 1970s, matured to the level of well-known textbooks (Bryce S. DeWitt 1975, N. D. Birrell and P. C. W. Davies 1982,Leonard Parker and David Toms 2009,Robert M. Wald 1994, S. A. Fulling 1989, A. Fabbri and J. Navarro-Salas 2005), but there are surprising new developments still being found. I am interested in these exciting aspects. I have focused my efforts on exploring the Bogoliubov formalism of acceleration radiation in the simple mathematical setting of flat spacetime. While quantum field theory in flat spacetime is all that is needed to derive the Unruh effect, the derivation of the Hawking effect from the Unruh effect exemplifies the close connection to curved spacetime. Strongly tied to my thesis research on the dynamical Casimir effect where the imposition of a boundary is allowed to accelerate, the Bogoliubov formalism is used to describe the appearance of particles and energy. Indeed, the Bogoliubov transformation, in which an initial canonical commutation relation algebra is transformed to a final representation, used in the dynamical Casimir effect, is the same formalism utilized in both the Hawking and Unruh effects. The Bogoliubov coefficients are normally taken to be global quantities, often in connection with late time limits, but my work has localized the coefficients with wave packets, rendering them useful for all times. As an investigation into the nonequilibrium particle production effects that occur during acceleration, this work has successfully adapted wave packetization to the dynamics. Developing exact moving mirrors models in 1+1 dimensional flat spacetime to deal with these non-thermal effects have allowed for analytic treatments for the energy flux and Bogoliubov/particle counts. This work is done in collaboration with Charles Evans and Paul Anderson. |
General RelativitySpectral Dynamics
Moving mirrors are accelerated boundaries that create energy, particles, and entropy. They are simplified 1 + 1 versions of the dynamical Casimir effect. Interesting in their own right, they also act as toy models for black hole evaporation. Time dependent accelerating mirrors in flat spacetime can be mapped directly to collapsing black hole curved spacetimes. These moving mirrors models incorporate important quantum fluctuation amplifying effects, and studying them offer a laboratory for studying gravitational-like effects. The boundaries act like a gravitational field in the sense that they can red-shift the field modes. Since an extended period of gradual geometric disruption red-shifts field modes, it is an interesting question how to time evolve this process. The distorted modes in the mirror case happen suddenly upon reflection. Hawking first used wave packets in the black hole case to deal with the divergent integral that represented the total created particles due to a steady rate of emission continuing for an infinite time (S. W. Hawking 1975). Using wave packets on moving mirrors, I have solved the all-time spectral evolution question. Removal of Acceleration Singularities Recently, I have written a paper on the moving mirror case, with Anderson and Evans, called ‘Time Dependence of Particle Creation for Accelerating Mirrors’(Michael R. R. Good, Paul R. Anderson, and Charles R. Evans 2013). The particular mirrors that are time evolved are interesting because they asymptotically approach inertial motion. Long after acceleration has stopped, the field modes may continue to incur red-shifting. These trajectories are distinct from previously well- studied solutions. They also have advantages over spliced motions, infinite accelerated motions and late time asymptotic motions. Some of these asymptotically inertial mirrors correspond in curved spacetime to what is known as a remnant (Frank Wilczek 1993), anticipated because of their predicted inertial red-shifting character. Avoiding thepathologies associated with horizons, asymptotically inertial mirrors are capable of being time evolved using wave packetization methods. The major result obtained after time evolving the process of particle creation using wave packets is a spectral history throughout the motion of the particular mirror. |
Quantum Fields in Curved Spacetime Appearance of Negative Energy Flux
It is also interesting that negative energy flux is emitted when the mirror has no horizon or infinite asymp-totic acceleration. Emission of negative energy by mirrors and detectors has been studied before in QFT, but they are not well known (N. D. Birrell and P. C. W. Davies 1982). Gaining a deeper understanding of the negative energy fluxes that occur during deacceleration may be fruitful. As localized particle production is always positive, there is a seemingly interesting discrepancy in how these negative energy fluxes relate. Enhanced correlation ratio functions occur during periods of negative energy emission and the state becomes more ordered than the vacuum, resulting in negative mirror entropy. The quantum purity of the evolution of the initial state into a final state is maintained in these asymptotically inertial cases. The cost of this purity is the emission of the negative energy flux. It is interesting to note that for mirrors that accelerate forever, producing horizons, no negative energy flux production occurs. While this project incorporates asymptotically inertial trajectories, a second project will be completed which will incorporate trajectories with infinite asymptotic acceleration. In addition to these works, I have presented this and closely related subjects at the 13th Eastern Gravity Meeting at North Carolina State University and in talks at the University of North Carolina, the CERN summer school at the Institute of Advanced Studies in Singapore, the GR20 conference in Poland, and other places (Korea, Vietnam, Germany,Taiwan, Washington, Kentucky, New York, etc). Further work towards the link with gravity, in particular discussing the details of time evolution of infinitely accelerated mirrors, and introducing new exactly solvable trajectories -of which few exist (Robert D. Carlitz and Raymond S. Willey 1987, W. R. Walker 1985,W. R. Walker and P. C. W. Davies 1982) is forthcoming. Phase Dynamics In collaboration with Kerson Huang and Chi Xiong, and others (Chi Xiong, Michael R. R. Good, Yulong Guo, Xiaopei Liu, and Kerson Huang 2014)., I am exploring a ‘superfluid universe’ model that focuses on the phase dynamics of complex scalar fields. Since the vacuum is filled with quantum complex scalar fields, we suspect their phase dynamics play an important role the early universe and ulti-mately, astrophysical contexts. The phase dynamics lead to superfluidity, vorticity, and quantum turbulence. From these ingredients an early universe fractal vortex tangle emerges, and it is proposed that it grows, and then decays. Matter can be created through the reconnection of vortex lines, a process necessary for its maintenance. This model has predictions for the later universe, including galactic voids, dark matter, non-thermal filaments, and cosmic jets. Our model (Kerson Huang, Hwee-Boon Low, and Roh-Suan Tung 2011-2012), consists of a set of closed cosmological equations based on Einstein’s equation with Robertson-Walker metric that describes a uniform cosmos. In order to obtain a self-consistent initial-value problem, it is necessary to use a complex scalar field that has an asymptotically free potential. We use the Halpern-Huang potential (Kenneth Halpern and Kerson Huang 1996) which is asymptotically free and is obtained through renormalization-group analysis in QFT. Quantum turbulence is described by a uniform vortex-line density, with dynamics governed by Vinen’s equation established in liquid helium. These equations describe the big-bang expansion driven by the scalar field on the one hand, and the vortex-matter dynamics on the other. These two aspects decouple from each other, due to a vast difference in energy scales. The lifetime of the vortex tangle gives a reasonable quantitative account of the era of cosmic inflation. Beyond the inflation era, the model ceases to be valid and the usual hot big bang theory takes over, but the universe remains a superfluid, and vortex activities persist. Main predictions are the following: 1. The universe expands at an accelerated rate, and therefore exhibits dark energy. The radius of the universe obeys a power law, which implies an equivalent cosmological constant that decays like a power and this avoids the fine-tuning problem. 2. The power law predicts a simple relation for the galactic redshift. Comparison with data leads to the speculation that the universe experienced a crossover transition, which was completed about 7 billion years ago. 3. Remnant vortex lines in the post-inflation universe have core sizes that expand with the universe, and in the 14 billion years since have reached hundreds of millions of light years, and are manifested as voids in the galactic distribution. 4. A stellar distribution may appear as a random potential to the underlying superfluid and will pin it, according to the theory of Huang and Meng (Kerson Huang and Hsin-Fei Meng 1992) and drag it along in its rotation. This will give galaxies extra moments of inertia perceived by us as dark matter. 5. Between the rotating superfluid and the stationary background is a boundary layer laced with vortex lines, which may help explain the non-thermal filaments observed near the center of our galaxy. 6. Occasional reconnection of remnant vortex lines would create two opposite jets of energy which may help explain gamma-ray bursts and cosmic jets of matter. |
QUANTUM COSMOLOGY
Salient Ongoing Work
Black Holes and Quantum Vortexes For those who are unfamiliar, gravitation and quantum theory have yet to be reconciled. Often, exotic circumstances surround those places in nature where both theories are needed, i.e. the Big Bang and black hole singularities. One interesting possibility where gravity meets quantum, is the appearance of tiny quantum whirlpools formed from the gravitation of a rotating collapsed star. Quantum vortexes are the tiniest torna- does known to exist in nature. They are famously found in very cold rotating liquid helium. Quantum fields exist near black holes and when the black holes rotate, those quantum fields exhibit a characteristic signature of superfluidity: quantized circulation. My collaborators and I are the first to find this curious phenomenon of gravitationally induced quantum vortexes (Michael R. R. Good, Chi Xiong, Alvin J. K. Chua, and Kerson Huang 2014) and we are currently writing a longer-type man uscript to fully explain the details of this frame-dragging geometric quantum creation effect. Black Holes and Springs Current efforts are directed toward a publication quality manuscript of work that found a close connection between springs and black holes. Perhaps springs and black holes, as central objects of study in both quantum theory and general relativity respectively, have more in common than is known. It was found (Michael R. R. Good and Yen Chin Ong 2014) that a (3 + 1)-dimensional asymptotically flat Kerr black hole angular speed Ω+ can be used to define an effective spring constant, k = mΩ2+ Its maximum value is the Schwarzschild surface gravity, k =k , which rapidly weakens as the black hole spins down and the temperature increases. The Hawking temperature of the rotating black hole is then expressed in terms of the spring constant:k 2πΤ=K-k Hooke’s law, in the extremal limit, provides the force F = 1/4, which is consistent with the conjecture of maximum force in general relativity. It’s important to note that this spring-black hole expression involves all the well-known fundamental constants, ¯ħ, G, c,kb; and may signify a deep connection between gravity (black holes) and the quanta (simple harmonic oscillator). |