Exploring the Relationship between Math and Science

In summary, QED and QCD are theories based on QFT, which is a general term for any theory which involves a field (something defined at every point in space and time) that is acted on with quantum operators. QED is based on the invariance of a local phase transformation of the fields according to the group U(1), while QCD is based on the invariance of a local quark-gluon field. To study QED and QCD, one must first know QFT well.
  • #1
Matterwave
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How are they related? Can you derive one from another, or are they separate fields of study?
 
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  • #2
QED, and QCD and QFD are theories based on QFT.
 
  • #3
QFT = "Quantum Field Theory" sort of a general term for any theory which involves a field (something defined at every point in space and time) that is acted on with quantum operators.
QED = "Quantum Electrodynamics" which is one example of a quantum field theory, where the fields are the electric and magnetic fields that arise from electrical charges and currents.
QCD = "Quantum Chromodynamics" which is another example of a quantum field theory, where the field comes from the "color charges" on quarks (and gluons I suppose).
 
  • #4
One can say something about the relation QED vs. QCD, QED is based on the invariance of a local phase transformation of the fields according to the group U(1). One starts with a free lagrangian of fermions (no interactions) and by demanding this local invariance, one has to include interactions. This is called a Gauge Theory, and QCD is also a gauge theory, but with SU(3) group for the local phase transformations.

In order to stody QED and QCD, one has to study QFT first. And very very often, QED is assumed to be know in quite detail before you attempt to learn QCD. You can think of QFT as the analogy with the Schrödinger equation in QM. In Schrödinger equation, the potential is unknown, and you can use potentials to fit a known phenomenon. Examples: The Hydrogen Atom, use a Coulomb potential. For semiconductors, use a step potential. Etc. In Quantum Field theory, you do in a similar way, you include the fields, fermions and/or boson fields, and interaction terms, and then you start to calculate observables and see if they fit with experiments. Also, one would like to have underlying symmetries, like these local phase transformations.
 
  • #5
Ok, thanks. :)
 

FAQ: Exploring the Relationship between Math and Science

What is the relationship between math and science?

The relationship between math and science is often described as inseparable. Math is the language of science, providing a way to quantify and analyze natural phenomena. Many scientific concepts, such as laws and equations, are based on mathematical principles and are used to explain and predict the behavior of the natural world. In turn, science also helps to advance and apply mathematical theories and concepts.

How is math used in science?

Math is used in science in various ways. It provides a way to measure and analyze data, make predictions, and create models and theories. In fields like physics and chemistry, math is used to develop equations and formulas to describe and understand the behavior of matter and energy. In biology and ecology, math is used to analyze population growth and distribution. Essentially, math is used in science to provide a quantitative and objective approach to understanding the natural world.

Can you give an example of how math and science are related?

One example of the relationship between math and science is in the study of gravity. The law of gravity, formulated by Sir Isaac Newton, uses mathematical equations to explain the force of attraction between two objects. This law has been crucial in understanding and predicting the motion of planets and other celestial bodies, and has even been used to send spacecraft to explore our solar system.

Why is it important to explore the relationship between math and science?

Exploring the relationship between math and science is important because it helps us to understand the fundamental principles that govern the natural world. By studying the connections between these two disciplines, we can gain a deeper understanding of how our universe works and make advancements in various fields of science. This knowledge is also essential in solving real-world problems and developing technologies that improve our lives.

How can we encourage more students to pursue careers in math and science?

To encourage more students to pursue careers in math and science, it is important to make these subjects more accessible and engaging. This can be done by incorporating real-world applications and hands-on experiments in the classroom, providing mentorship opportunities, and highlighting the diverse career options in these fields. Additionally, promoting the importance and relevance of math and science in our everyday lives can also inspire students to pursue these subjects further.

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