#### Quantum Fields

*Quantum Fields *are the fundamental entities of the universe.

The fields are observed as *particles*, leaving tracks and traces in particle accelerators and cosmic ray detectors.

#### Scientists on Quantum Fields

###### Julian Seymour Schwinger, winner of Nobel Prize for developing QED

…these two distinct classical concepts [particles and fields] are merged and become transcended in something that has no classical counterpart – the quantized field that is a new conception of its own, a unity that replaces the classical duality.

###### Frank Wilczek, winner of Nobel Prize for discoveries leading to QCD

The Core theory, which summarizes our best current understanding of fundamental processes, is formulated in terms of quantum fields. Particles appear as secondary consequences; they are localized disturbances in the primary entities – that is, in quantum fields.

###### Don Little, particle physicist at Fermi National Accelerator Laboratory

Quantum fields are really a mind-bending way of thinking. Everything—and I mean everything—is just a consequence of many infinitely-large fields vibrating. The entire universe is made of fields playing a vast, subatomic symphony

###### Sean Carroll, from The Particle at the End of the Universe

- “Conceptually, a field is the opposite of a particle. A particle has a specific location in space, while a field exists at every point in space. Quantum mechanics brought the two concepts together. Long story short: Everything is made of fields, but when we look at them closely we see particles.
- When quantum mechanics gets applied to fields, we end up with “quantum field theory,” which is the basis for our modern explanations of reality at its most fundamental level. According to quantum field theory, when we observe a field carefully enough we see it resolve into individual particles—although the field itself is real. (The field actually has a wave function describing the probability of finding it with any particular value at each point in space.) Think of a TV set or computer monitor, which seems to display a smooth picture from a distance, but close up we find that it’s actually a collection of tiny pixels. On a quantum TV set there really is a smooth picture, but when we look closely at it we can only ever observe it as pixels.
- Is matter made of particles or waves? Here’s the answer: Matter is really waves (quantum fields), but when we look at it carefully enough we see particles.”

**David Tong**, from his lecture on Quantum Fields: The Real Building Blocks of the Universe

- “According to our best laws of physics, the fundamental building blocks of Nature are not discrete particles at all. Instead they are continuous fluid-like substances, spread throughout all of space. We call these objects fields.
- If you look closely enough at electromagnetic waves, you’ll find that they are made out of particles called photons. The ripples of the electric and magnetic fields get turned into particles when we include the effects of quantum mechanics.
- But this same process is at play for all other particles that we know of. There exists, spread thinly throughout space, something called an electron field. Ripples of the electron field get tied up into a bundle of energy by quantum mechanics. And this bundle of energy is what we call an electron. Similarly, there is a quark field, and a gluon field, and Higgs boson field. Every particle in your body — indeed, every particle in the Universe — is a tiny ripple of the underlying field, moulded into a particle by the machinery of quantum mechanics.”

#### Concept of a Field

- A
*field*is a physical quantity that has a numeric value at every point in space, the values changing over time. - Values can be
- Scalars (single numbers)
- E.g. Temperature

- Vectors (having magnitude and direction)
- E.g. Gravitational Field, Electric Field, Magnetic Field

- Tensors (matrices of numbers)
- E.g. Stress-Energy Tensor of General Relativity

- Scalars (single numbers)
- Michael Faraday developed the concept of a field in the first half of the 19th century.
- James Clerk Maxwell later developed the mathematics for fields
- Two-minute Video What is a field, by George Musser