In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases. It is usually denoted by H, also Ȟ or Ĥ. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.
The Hamiltonian is named after William Rowan Hamilton, who also created a revolutionary reformation of Newtonian mechanics, now called Hamiltonian mechanics, that is important in quantum physics.

https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)

In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative.[1] This problem raises the question of what time really is in a physical sense and whether it is truly a real, distinct phenomenon. It also involves the related question of why time seems to flow in a single direction, despite the fact that no known physical laws seem to require a single direction.

https://en.wikipedia.org/wiki/Problem_of_time

The Wheeler–DeWitt equation[1] is a field equation. It is part of a theory that attempts to combine mathematically the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity. In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called ‘problem of time’.[2] More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergman-Komar “group” (which is the diffeomorphism group on-shell.

https://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation

cGh physics refers to the mainstream attempts in physics to unify relativity, gravitation and quantum mechanics, in particular following the ideas of Matvei Petrovich Bronstein and George Gamow. The letters are the standard symbols for the speed of light (c), the gravitational constant (G), and Planck’s constant (h).
If one considers these three universal constants as the basis for a 3-D coordinate system and envisions a cube, then this pedagogic construction provides a framework, which is referred to as the cGh cube, or physics cube, or cube of theoretical physics (CTP). This cube can used for organizing major subjects within physics as occupying each of the eight corners. The eight corners of the cGh physics cube are:
Classical mechanics (_,_,_)
Special relativity (c,_,_), Gravitation (_,G,_), Quantum mechanics (_,_,h)
General relativity (c,G,_), Quantum field theory (c,_,h), Non-relativistic quantum theory with gravity (_,G,h)
Theory of everything, or relativistic quantum gravity (c,G,h)
Other cGh subjects include Planck units, Hawking radiation and black hole thermodynamics.
While there are several other physical constants, these three are given special consideration, because they can be used to define all Planck units and thus all physical quantities. The three constants are therefore used sometimes as a framework for philosophical study and as one of pedagogical patterns.[5]

Matvei Petrovich Bronstein (Russian: Матвей Петрович Бронштейн, December 2 [O.S. November 19] 1906, Vinnytsia – February 18, 1938) was a Soviet theoretical physicist, a pioneer of quantum gravity, author of works in astrophysics, semiconductors, quantum electrodynamics and cosmology, as well as of a number of books in popular science for children.
He introduced the cGh scheme for classifying physical theories. “After the relativistic quantum theory is created, the task will be to develop the next part of our scheme, that is to unify quantum theory (with its constant h), special relativity (with constant c), and the theory of gravitation (with its G) into a single theory.”
He was married to Lydia Chukovskaya, a writer, prominent human rights activist, and a friend of Andrei Sakharov.
During the Great Purge, in August 1937 Bronstein was arrested. He was convicted by a list trial (“по списку”) in February 1938 and executed the same day in a Leningrad prison. His wife was told that he was sentenced to 10 years of labor camps without the right of correspondence.
Bronstein’s books for children “Solar matter” (Солнечное вещество), “X Rays” (Лучи X), “Inventors of Radio” (Изобретатели радио) were republished after he had been rehabilitated in 1957.
The “Bronstein Prize in Loop Quantum Gravity” is offered to Post-doctoral scholars in the field, the inaugural winner of which was Eugenio Bianchi in 2013.

The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows a physicist to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these are coordinate space or Feynman path integrals), than the Hamiltonian. Possible downsides of the approach include that unitarity (this is related to conservation of probability; the probabilities of all physically possible outcomes must add up to one) of the S-matrix is obscure in the formulation. The path-integral approach has been proved to be equivalent to the other formalisms of quantum mechanics and quantum field theory. Thus, by deriving either approach from the other, problems associated with one or the other approach (as exemplified by Lorentz covariance or unitarity) go away.
The path integral also relates quantum and stochastic processes, and this provided the basis for the grand synthesis of the 1970s, which unified quantum field theory with the statistical field theory of a fluctuating field near a second-order phase transition. The Schrödinger equation is a diffusion equation with an imaginary diffusion constant, and the path integral is an analytic continuation of a method for summing up all possible random walks.
The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Brownian motion. This idea was extended to the use of the Lagrangian in quantum mechanics by P. A. M. Dirac in his 1933 article. The complete method was developed in 1948 by Richard Feynman. Some preliminaries were worked out earlier in his doctoral work under the supervision of John Archibald Wheeler. The original motivation stemmed from the desire to obtain a quantum-mechanical formulation for the Wheeler–Feynman absorber theory using a Lagrangian (rather than a Hamiltonian) as a starting point.

https://en.wikipedia.org/wiki/Path_integral_formulation

https://en.wikipedia.org/wiki/J._Robert_Oppenheimer

https://en.wikipedia.org/wiki/Geon_(physics)

https://en.wikipedia.org/wiki/Fat_Man

https://en.wikipedia.org/wiki/Hugh_Everett_III

https://en.wikipedia.org/wiki/Charles_W._Misner

Hans Albrecht Bethe (German: [ˈhans ˈalbʁɛçt ˈbeːtə]; July 2, 1906 – March 6, 2005) was a German-American nuclear physicist who made important contributions to astrophysics, quantum electrodynamics and solid-state physics, and won the 1967 Nobel Prize in Physics for his work on the theory of stellar nucleosynthesis.^[1][2]

For most of his career, Bethe was a professor at Cornell University.^[3] During World War II, he was head of the Theoretical Division at the secret Los Alamos laboratory which developed the first atomic bombs. There he played a key role in calculating the critical mass of the weapons and developing the theory behind the implosion method used in both the Trinity test and the “Fat Man” weapon dropped on Nagasaki in August 1945.

After the war, Bethe also played an important role in the development of the hydrogen bomb, though he had originally joined the project with the hope of proving it could not be made. Bethe later campaigned with Albert Einstein and the Emergency Committee of Atomic Scientists against nuclear testing and the nuclear arms race. He helped persuade the Kennedy and Nixon administrations to sign, respectively, the 1963 Partial Nuclear Test Ban Treaty and 1972 Anti-Ballistic Missile Treaty (SALT I).

His scientific research never ceased and he was publishing papers well into his nineties, making him one of the few scientists to have published at least one major paper in his field during every decade of his career – which, in Bethe’s case, spanned nearly seventy years. Freeman Dyson, once one of his students, called him the “supreme problem-solver of the 20th century”.^[4]

https://en.wikipedia.org/wiki/Hans_Bethe