EPSRC Reference: 
EP/V002821/1 
Title: 
PT symmetric field theory 
Principal Investigator: 
Sarkar, Professor S 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Physics 
Organisation: 
Kings College London 
Scheme: 
Standard Research 
Starts: 
01 July 2021 
Ends: 
31 March 2025 
Value (£): 
477,769

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Physical systems are described by a quantity called the Hamiltonian. In conventional
quantum physics two kinds of Hamiltonians are used,
(i) Hermitian Hamiltonians, which govern the behaviour of isolated
systems, and (ii) nonHermitian Hamiltonians, which have been used to describe
the behaviour of systems in contact with the environment.
Hermitian Hamiltonians describe idealised systems in equilibrium whose total
energy and probability are conserved; the energy levels of such systems are real.
NonHermitian Hamiltonians in general receive energy from and/or dissipate energy
into their environment, so they are not typically in equilibrium, their energy and
probability are not conserved, and their energy levels are complex, due to the levels being unstable.
This proposal concerns a category of socalled PTsymmetric
Hamiltonians, which share properties of both Hermitian and nonHermitian
Hamiltonians, being intermediate between conservative and dissipative systems.
Like nonHermitian systems,PTsymmetric systems are not isolated, but their contact
with the environment is constrained so that gain from the environment
and loss to the environment are exactly balanced. Thus, while they
are not isolated, PTsymmetric systems in equilibrium behave
like Hermitian systems and their energy levels are real. However,
unlike Hermitian systems, PTsymmetric systems can exhibit
a transition from an unbroken equilibrium phase, where the energies
are real, to a broken nonequilibrium phase where the energies are
complex. Hermitian systems can never have complex energies and thus
cannot have such a phase transition. The PT phase transition is a characteristic
signature that has been observed in experiments.
Quantum mechanics is essential for describing the physics of particles and involves a
finite number of degrees of freedom. However, particles are excitations of quantum fields,
which are defined over all space and time. Quantum field theories
have infinitely many degrees of freedom. Consequently the formulation of PTsymmetric
field theory is required to describe any fundamental theory involving PT symmetry.
Moreover, even within the framework of Hermitian quantum field theories, nonHermitian
PT symmetric features often emerge in calculations. These features tend to be dismissed,
either on the basis of nonrigorous mathematics related to prescriptions introduced to extract
finite numbers from divergent expressions in calculations,
or incompleteness of the physical model. This proposal investigates directly the role and
properties of PT symmetry in fundamental quantum field theories by investigating the following
questions:
1. Are there analogues in quantum field theory of the features that distinguish PTsymmetric
quantum mechanical systems from Hermitian quantum mechanics?
2.Are there any restrictions on the type of PTsymmetric field theories that show analogous features?
3. Can nonHermitian features, which arise due to divergences in Hermitian field theories, be dealt
with by procedures within the framework of PTsymmetric quantum field theory?
4. Can PTsymmetric field theories lead to new possibilities for models of fundamental physics, which,
in low number of spatial dimension, may be realised in the laboratory?
These are the questions that the project aims to answer.

Key Findings 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Potential use in nonacademic contexts 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Impacts 
Description 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk 
Summary 

Date Materialised 


Sectors submitted by the Researcher 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Project URL: 

Further Information: 

Organisation Website: 
