# Quantum Mechanics: QM, QCD, QED Explained

• Swapnil
In summary, the realm of quantum mechanics covers a wide range of problems and theories, including classical non-relativistic mechanics, quantum field theory, and the standard model. This includes applications such as Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD). However, while quantum mechanics is a well-founded theory, quantum field theory is still mathematically messy and has not been fully formulated. Additionally, the metric of spacetime in general relativity has not yet been successfully incorporated into quantum theory.
Swapnil
Hi, I was wondering, what does the realm of quantum mechanics cover? I mean, I always hear a talk about how it would be a holy grail of physics if we could somehow combine GR and QM. But what about QCD, QED, and other theories. Why aren't they mentioned? Is it because QM encompasses them?

Swapnil said:
Hi, I was wondering, what does the realm of quantum mechanics cover? I mean, I always hear a talk about how it would be a holy grail of physics if we could somehow combine GR and QM. But what about QCD, QED, and other theories. Why aren't they mentioned? Is it because QM encompasses them?

Well there are some confusions in terminology.

"Quantum theory" QT can be seen as a rather abstract formalism of Hilbert spaces, a unitary evolution on it, observable Hermitean operators and so on ; or in equivalent formulations, using path integrals and the like.

One usually first encounters it, applied to a specific kind of problems, which is that of classical non-relativistic mechanics. This is then called "quantum mechanics" QM. But sometimes, one understands by quantum mechanics, quantum theory.

If you (try to) apply quantum theory to another kind of problems, namely those of classical relativistic fields, then you obtain quantum field theory QFT. By chosing a specific set of fields, for instance, the Maxwell equations, Dirac's equation and so on, you can cook up different applications of QFT. The first one was applied to the Maxwell equations and the electron field (Dirac equation). It is called Quantum Electrodynamics QED. Another one, quite more involved, with more fields and tricks, is called the Weinberg-Salam model of electroweak interactions. It incorporates in fact, QED.

Still another one is about the fields of gluons and quarks, and is called quantum chromodynamics QCD.

Both together are called "the standard model". It's a specific application of QFT to a certain set of fields, which, itself, is a specific application of QT to fields.

However, it must be said that in as much as quantum mechanics is a totally mathematically well-found theory, the same cannot be said about QFT. It is mathematically quite messy and nobody has ever found a way to completely make a rigorous formulation of it.

There is a "classical field" however, which has resisted any "attack" by quantum theory, and that is the metric of spacetime (general relativity).
There, things are not only mathematically messy. One doesn't even know how to start, and how to get numbers out.

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Quantum mechanics is a fundamental theory in physics that describes the behavior of particles at a very small scale, such as atoms and subatomic particles. It is a highly successful theory that has been verified by numerous experiments and is essential for understanding the behavior of matter and energy at this scale.

Quantum mechanics covers a wide range of phenomena, including the behavior of particles in different energy states, the uncertainty principle, and wave-particle duality. It also provides a framework for understanding the behavior of atoms, molecules, and other systems made up of particles.

In terms of other theories like QCD (quantum chromodynamics) and QED (quantum electrodynamics), these are specific theories that fall under the umbrella of quantum mechanics. QCD is a theory that describes the behavior of subatomic particles called quarks and gluons, while QED explains the behavior of particles interacting through the electromagnetic force.

The reason why these theories are not often mentioned in discussions about the "holy grail" of physics is that they are already well-integrated into the framework of quantum mechanics. In fact, many physicists are actively working on combining these theories with general relativity (GR) to create a unified theory of physics.

Overall, quantum mechanics covers a vast range of phenomena and is essential for understanding the behavior of particles at a small scale. QCD, QED, and other theories are all important components of quantum mechanics and are actively being studied and integrated into our understanding of the universe.

## 1. What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior and interactions of particles at the subatomic level. It explains the fundamental principles that govern the behavior of matter and energy on a very small scale, such as atoms and subatomic particles.

## 2. What is the difference between QM, QCD, and QED?

QM, QCD, and QED are all different theories within the field of quantum mechanics. QM (Quantum Mechanics) is the overarching theory that explains the behavior of particles on a quantum level. QCD (Quantum Chromodynamics) is a theory that describes the interactions between subatomic particles called quarks, which make up protons and neutrons. QED (Quantum Electrodynamics) is a theory that explains the interactions between particles with electric charge, such as electrons and photons.

## 3. How does quantum mechanics differ from classical mechanics?

Classical mechanics is the branch of physics that explains the behavior of larger objects, such as planets and cars, using Newton's laws of motion. Quantum mechanics, on the other hand, explains the behavior of particles at a subatomic level, where classical mechanics does not apply. In quantum mechanics, particles can exist in multiple states simultaneously and behave unpredictably, unlike classical particles.

## 4. What implications does quantum mechanics have on our everyday lives?

Quantum mechanics has many practical applications, including the development of transistors and computer chips, which are essential components of modern technology. It also plays a role in fields such as chemistry, material science, and medicine. However, its more abstract concepts, such as superposition and entanglement, have not yet been fully understood and have sparked philosophical debates.

## 5. Is quantum mechanics a complete theory?

Quantum mechanics is currently the most accurate and successful theory we have to explain the behavior of particles at a subatomic level. However, it is not a complete theory and has some unresolved paradoxes and inconsistencies, such as the measurement problem and the conflict with general relativity. Scientists continue to research and develop new theories, such as string theory, to try and reconcile these issues and create a more complete understanding of the universe.

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