Should a "static final Logger" be declared in UPPER-CASE?

The logger reference is not a constant, but a final reference, and should NOT be in uppercase. A constant VALUE should be in uppercase.

private static final Logger logger = Logger.getLogger(MyClass.class);

private static final double MY_CONSTANT = 0.0;

To add more value to crunchdog's answer, The Java Coding Style Guide states this in paragraph 3.3 Field Naming

Names of fields being used as constants should be all upper-case, with underscores separating words. The following are considered to be constants:

1. All static final primitive types (Remember that all interface fields are inherently static final).
2. All static final object reference types that are never followed by "." (dot).
3. All static final arrays that are never followed by "[" (opening square bracket).

Examples:

MIN_VALUE, MAX_BUFFER_SIZE, OPTIONS_FILE_NAME

Following this convention, logger is a static final object reference as stated in point 2, but because it is followed by "." everytime you use it, it can not be considered as a constant and thus should be lower case.

From effective java, 2nd ed.,

The sole exception to the previous rule concerns “constant fields,” whose names should consist of one or more uppercase words separated by the underscore character, for example, VALUES or NEGATIVE_INFINITY. A constant field is a static final field whose value is immutable. If a static final field has a primitive type or an immutable reference type (Item 15), then it is a constant field. For example, enum constants are constant fields. If a static final field has a mutable reference type, it can still be a constant field if the referenced object is immutable.

In summary, constant == static final, plus if it's a reference (vs. a simple type), immutability.

Looking at the slf4j logger, http://www.slf4j.org/api/org/slf4j/Logger.html

It is immutable. On the other hand, the JUL logger is mutable. The log4j logger is also mutable. So to be correct, if you are using log4j or JUL, it should be "logger", and if you are using slf4j, it should be LOGGER.

Note that the slf4j javadocs page linked above has an example where they use "logger", not "LOGGER".

These are of course only conventions and not rules. If you happen to be using slf4j and you want to use "logger" because you are used to that from other frameworks, or if it is easier to type, or for readability, go ahead.

I like Google's take on it (Google Java Style)

Every constant is a static final field, but not all static final fields are constants. Before choosing constant case, consider whether the field really feels like a constant. For example, if any of that instance's observable state can change, it is almost certainly not a constant. Merely intending to never mutate the object is generally not enough.

Examples:

// Constants
static final int NUMBER = 5;
static final ImmutableList<String> NAMES = ImmutableList.of("Ed", "Ann");
static final Joiner COMMA_JOINER = Joiner.on(',');  // because Joiner is immutable
static final SomeMutableType[] EMPTY_ARRAY = {};
enum SomeEnum { ENUM_CONSTANT }

// Not constants
static String nonFinal = "non-final";
final String nonStatic = "non-static";
static final Set<String> mutableCollection = new HashSet<String>();
static final ImmutableSet<SomeMutableType> mutableElements = ImmutableSet.of(mutable);
static final Logger logger = Logger.getLogger(MyClass.getName());
static final String[] nonEmptyArray = {"these", "can", "change"};

If you are using an automated tool to check your coding standards and it violates said standards then it or the standards should be fixed. If you're using an external standard, fix the code.

The convention in Sun Java is uppercase for public static constants. Obviously a logger is not constant, but represents a mutable thing ( otherwise there would be no point calling methods on it in the hope that something will happen ); there's no specific standard for non-constant final fields.