Meaning of h.c. in Lagrangians (& elsewhere?)

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In summary, "h.c." in Lagrangians (and elsewhere) denotes the addition of hermitian conjugate terms, which ensures the Hamiltonian is a hermitian operator. This notation is commonly used and serves as a shorthand to omit half the terms present. It is not unique to particle physics.
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Meaning of "h.c." in Lagrangians (& elsewhere?)

I am fairly new to particle physics and am puzzled by an abbreviation I often see in Lagrangians here (though it may not be particular to that application): " + h.c." is tacked on after other terms. What does this denote? Apologies if I've missed something very simple, and thanks for the help either way!
 
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This is not unique to particle physics. All it means is that there are additional terms which are the hermitian conjugate of the terms that have already been written.

Zz.
 
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What Zz said. The Hamiltonian should be a hermitian operator, but note that if we have any (well-behaved) operator A, then A + Adagger is hermitian. So the notation is both a convenient way of making sure we have a hermitian operator and a convenient shorthand to omit half the terms present.
 

What does h.c. stand for in Lagrangians?

h.c. stands for "Hermitian conjugate", which is a mathematical operation used to construct complex conjugates of expressions in quantum mechanics. In Lagrangians, h.c. is often used to represent the complex conjugate of a term.

Why is h.c. used in Lagrangians?

In Lagrangian mechanics, h.c. is used to ensure that the Lagrangian (a function that describes the dynamics of a physical system) is invariant under certain transformations. This is necessary for the equations of motion to be consistent with the principles of quantum mechanics.

Where else is h.c. used besides Lagrangians?

Aside from Lagrangians, h.c. is also commonly used in other areas of physics, such as quantum field theory, particle physics, and condensed matter physics. It is also used in mathematics, particularly in complex analysis and linear algebra.

How is h.c. represented in mathematical notation?

In mathematical notation, h.c. is denoted by a superscript dagger (†) or an asterisk (*), depending on the context. For example, if z is a complex number, then the h.c. of z would be represented as z† or z*.

What is the relationship between h.c. and the complex conjugate?

The Hermitian conjugate (h.c.) of a complex number is equal to its complex conjugate. However, in quantum mechanics, h.c. is more commonly used to refer to the complex conjugate of a term or expression within a larger equation or function.

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